Math Practice Problems to Teach Strategies for Eighth Grade

 

8S-9d) Strategy: Guess, check, and revise Answer: Clowns - 140, magicians - 420, fire-eaters - 35, people in gorilla suits - 140, jugglers - 560

Business was booming for the Sensational Events Company. During the past year they supplied 1295 entertainers for parties. They sent three times as many magicians as clowns, 25% as many fire-eaters as clowns, one-third as many people in gorilla suits as magicians, and a number of jugglers equal to the combined number of clowns and magicians. How many magicians, clowns, fire-eaters, people in gorilla suits, and jugglers had Sensational Events supplied for parties during the past year?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-9c) Strategy: Guess, check, and revise Answer: radishes - 129, zucchini - 387, head of lettuce - 215, potatoes - 349, artichokes - 258, carrots - 43

The First international Vegetable Extravaganza (FIVE) Program was almost finished. Zachary Zucchini was reporting on the attendance figures to Ruby Radish. He said that there were three times as many zucchini as radishes present, 5/9 as many heads of lettuce as zucchini, five more potatoes than the combined number of heads of lettuce and radishes, one half as many artichokes as zucchinis and radishes combined, and that the number of carrots was 20% of the heads of lettuce. He said they had a marvelous turnout of 1381 vegetables in all. How many of each kind of vegetable attended the conference?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-9b) Strategy: Guess, check, and revise Answer: Farley - 40, Floyd - 5, Franny - 10, Frank - 25, Fiona - 20, Festus - 15

It's feeding time in the jungle, and the Flytrap children are hungry. Their mother, Venus, has been gathering flies for her children's upturned mouths. "Remember, children, you must eat all your dinner, or no dessert." She needn't worry! Yesterday, the six Flytrap brothers and sisters ate 115 flies altogether. Farley ate four times the number of flies that Franny ate. Fiona managed to snap up half the number of flies that Farley ate. Frank gulped down as many flies as Fiona and Floyd together. Franny ate twice as many as Floyd. Festus ate five fewer flies than Fiona, and Floyd ate one-eighth as many as Farley. (Floyd is a picky eater.) How many flies did each child eat?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-9a) Strategy: Guess, check, and revise Answer: 1^st day -250, 2^nd day - 125, 3^rd day - 400, 4^th day - 100, 5^th day - 125

The king's messengers are exhausted. It seems that the prince met an especially beautiful lady at the ball last week. After one dance with her, the royal clock chimed midnight and she ran off, leaving a small slipper behind. The prince wanted the messengers to find his mystery lady! For five full days the messengers went from door to door, trying to squeeze every female foot in the kingdom into the slipper. They tried twice as many feet on the first day as on the second day. On the third day they tried 25 more feet than the combined number of feet that they tried on the first two days. On the fourth day they tried 25% as many feet as on the third day. On the last day they tried 25% more feet than they had on the fourth day. On the 1000th try, they found the foot that fit. How many feet did they attempt to fit the shoe on each day?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-8f) Strategy: Draw a picture Answer: 11

Scotty and Emma drive space shuttles between Tronzer and Auzum for ITS, the Intergalactic Transport System. That shuttle run takes 5 days one way. Scotty's spacecraft, a Tronzer Shuttle, departs from Tronzer at 10:00 A.M and arrives on Auzum at 10:00 A.M. five days later. Emma's spacecraft, an Auzum Shuttle, starts out from Auzum at 10:00 A.M. and arrives on Tronzer five days later. There are many shuttles flying that same run. At 10:00 A.M. every day of the year, one shuttle is departing from Tronzer and one shuttle is arriving on Tronzer; and, one shuttle is departing from Auzum and one shuttle is arriving on Auzum. How many Auzum Shuttles will Scotty see on one of his five-day runs from Tronzer?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-8e) Strategy: Draw a picture Answer: 1451

Tyrone's Fantastic Footwear uses tennis-playing chimps to advertise their high tops. The store carries shoes for a variety of sports. When Serena entered the store, a salesman ran up to announce that the store had 555 pairs of shoes with high tops, 730 pairs with striped laces, and 654 pairs of pastel-colored shoes. He said that 227 pairs were pastel with striped laces; 265 pairs were high tops with striped laces; 143 pairs were high tops and pastel; and 65 pairs were high tops, pastel, and had striped laces. The salesman added that they also had 277 special pairs that were plaid. How many pairs of shoes did Serena have to choose from?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-8d) Strategy: Draw a picture Answer: 6 + part of 7^th

As Clyde moves his broom around the circus ring, he thinks that he has finally found a job where he can make a clean sweep of things. Clyde is sweeping the ring where the lions perform in the Filbert Family Circus. The ring is 76 feet across and Clyde's broom is 3 feet wide. He starts at the outside edge and works his way to the middle, making circles around the ring. After sweeping three fourths of the ring, Clyde sees the lions coming with their trainer and scurries out of the ring. How many trips around the ring did he make?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-8c) Strategy: Draw a picture Answer: 8 hours; Larry skateboarding 24 miles & walking 12, Brett skateboarding 12 and walking 24

Larry and his brother Brett are stranded in the desert. Their car has broken down in the middle of the hot day, and it is 36 miles to the nearest town. "Looks like we'll have to leave the car and take turns with the canteen and the skateboard," Larry said gloomily. The brothers want to leave at the same time and arrive in town at the same time. Both Larry and Brett know that they skateboard at the same speed, 6 miles per hour. Larry walks at 3 miles an hour and Brett walks at 4 miles an hour. They make a plan to exchange the skateboard along the way, when necessary. They will always leave the skateboard on the hour, but neither one can wait for the other. How long did it take them to get to the town and how many miles did each one walk and each one skateboard?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-8b) Strategy: Draw a picture Answer: 14x24

Holly and Harlan took a shortcut home through the park. It was a warm day; so they parked their bikes and took a drink from the water fountain. While resting, they watched workmen putting in a huge flowerbed around a statue of George Washington. The flowerbed consisted of a series of rectangular borders surrounding the statue, with a different type of flower in each border. The base of the statue in the center was 12 feet by 2 feet, and each border was 3 feet wide. "Where do we plant the jonquils?" one of the workers shouted. The supervisor stuck his head around the base of the statue and responded, "In the border that has 8 times the area of this base." Holly looked at Harlan, puzzled. "Do you know what he's talking about?" she asked. "I'm not sure," answered Harlan, "but let's figure it out." What are the dimensions of that border?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-8a) Strategy: Draw a picture Answer: 330

It is the first annual Fretters' Convention, and musicians from all over the country have assembled to play their instruments. There will be concerts, contests, and jam sessions. Lizzy has come with her father, who is an amateur musician. Lizzy is milling about, looking at the musicians' plastic name tags, which are shaped like guitars, banjos, and ukeleles. She notices that 170 people at the convention play the guitar, 185 play the banjo, and 97 play the ukelele. Nineteen play no instrument at all, but are there just for the fun, like her. She observes that 87 people play guitar and banjo, 42 play ukelele and guitar, 48 play banjo and ukelele, and 36 people play all three instruments. How many people in all are attending the Fretters' Convention?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-7c) Strategy: Act out the problem or use objects Answer: Gats Bee - Barna Bee - Bay Bee; Vitamin Bee - Spelling Bee - Bar Bee; Walla Bee - Honey Bee - Toyn Bee

The Queen Bee was furious because several workers missed roll call again, and the clover in the field was in full bloom. "I bet they're hiding out in the TM room again," she said, as she set off to find them. Sure enough, there they were along with the youngest member of the hive, Bay Bee, watching, "Days of Our Hives." Coming up next was "Miami Lice.' Barna Bee was directly in front of the TM set; Spelling Bee was sitting between Vitamin Bee and Bar Bee and directly behind Barna Bee; Gats Bee was in front of Vitamin Bee; Toyn Bee was to the right of Honey Bee; and Walla Bee was in the back row, but not behind Bar Bee, because Bar was so tall that her exoskeleton hid the screen.   Where was everyone sitting in the television room?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-7b) Strategy: Act out the problem or use objects Answer: Paul - Donna - Dave - Allen - Peter - Marco - Irene - Lani - Michelle

When Lizzy came home from hockey practice, she asked her little sister, Malinda, if she had received any phone calls. "Yes, you got lots of calls," Malinda said. "Oh GREAT!" exclaimed Lizzy, who loved to talk on the phone. "Who called, and when did they call?" she asked. Malinda said, "Well, let me think - I didn't write it down, but I think I can remember. Paul called before Donna. Lani called next to last. Irene called between Marco and Lani. Allen called after Dave, and Peter called before Marco. Michelle called after Lani, and Donna called before Dave. And, oh yes, Allen called between Dave and Peter." What was the order in which Lizzy's friends called?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-7a) Strategy: Act out the problem or use objects Answer: shirt-beach towel-suntan lotion-beach bag-can of soda; Shorts-swimsuit-sunglasses-sandals-magazine

Kane works as a salesclerk at the Threads Swimshop. His manager asked him to arrange a shirt, a pair of shorts, a pair of sandals, a swimsuit, a beach towel, a beach bag, suntan lotion, a magazine, a can of soda pop, and a pair of sunglasses in a display case. When Kane finished the job, the suntan lotion was behind the sunglasses and to the left of the beach bag. The beach towel was between the shirt and the suntan lotion. The sunglasses were to the right of the shorts and swimsuit. The shorts were not in front of the beach towel. The can of soda pop was to the right of the beach bag, and the sandals were to the left of the magazine. Where was each product in the display case?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-6g) Strategy: Make a table or chart Answer: Armadillos - 2052; bats - 90; caterpillars - 91

Everyone knows that the swallows return to Mission San Juan Capistrano every year. What they don't know, however, is that Appletown, Boomtown, and Cocoontown also receive annual visits from the animal kingdom, beginning on January 1 of each year. Last year, on the first day 6 armadillos returned to Appletown, 10 bats returned to Boomtown, and 21 caterpillars returned to Cocoontown. On the second day 12 armadillos, 20 bats, and 16 caterpillars returned. The next day 8 armadillos, 18 bats, and 28 caterpillars returned. On the fourth day 16 armadillos, 28 bats, and 23 caterpillars returned. On the fifth day 12 armadillos, 26 bats, and 35 caterpillars returned. This rate of return continued until the 21st day, when 2,233 creatures returned. How many of them were armadillos, how many were bats, and how many were caterpillars?  Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-6f) Strategy: Make a table or chart Answer: 478

Water is scarce in the Kalahari desert, and biologists are counting the animals that come to one of the watering holes. They notice that the animals that are fierce enemies vary their schedules during the day, to avoid confrontations. The first day the biologists count 7 wildebeests, 4 elephants, 6 zebras, and 5 lions. On the second day they count 10 wildebeests, 2 elephants, 8 zebras, and 4 lions; on the third day 9 wildebeests, 6 elephants, 5 zebras, and 7 lions; on the fourth day 12 wildebeests, 4 elephants, 7 zebras, and 6 lions; and 11 wildebeests, 8 elephants, 4 zebras, and 9 lions on the fifth day. If this pattern continues, how many animals will they have counted altogether on the first day that they don't see any zebras?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-6e) Strategy: Make a table or chart Answer: Wed.

Professor Orion and Professor Polaris are working every night this month at the Mt. Olympus Observatory. On Monday night, during his shift from 8-10 P.M., Professor Orion notices 12 new stars. He finds 18 new stars on Tuesday, 30 on Wednesday, 36 on Thursday, and 48 on Friday. Professor Polaris, working the 10-12 P.M. shift, notices 18 new stars on Monday, 26 on Tuesday, 44 on Wednesday, 52 on Thursday, and 70 on Friday. If the professors continue to spot new stars at the same rate, during what day of the week will their combined total equal the number of days in a year?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-6d) Strategy: Make a table or chart Answer: only once, 120 days from today

Lourdes is excited because her family is planning a reunion. Lourdes lives on a farm and hasn't seen her cousins for several years. Everyone is arriving on different trains: one cousin from San Francisco, an aunt and a cousin from Los Angeles, an uncle and two cousins from Nevada, her grandmother from Colorado, and a grandfather from Boston. Because Lourdes lives in a small town, the train schedule is as follows: A train arrives from San Francisco every four days, one arrives from Los Angeles every ten days, one from Nevada every three days, one from Colorado every eight days, and one from Boston every fifteen days. Lourdes' relatives are trying to all arrive on the same day, because it is a long way from the train station to the farm. If the trains all arrived together today, when in the next 20 weeks could the family members all arrive on the same day?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-6c) Strategy: Make a table or chart Answer: 17 times

Poor Geppetto. After solving his problems with Pinocchio, he returns to his clock shop to find that his clocks are all off schedule. His clocks, some of which sound like train whistles, some like bells, some like cuckoos, and some like fire alarms, are all supposed to go off at the same time. However, the train whistle clocks are now going off every 9 minutes, the bell clocks every 3 minutes, the cuckoos every 6 minutes, and the fire alarm clocks every 4 minutes. If all the clocks have just gone off at the same time, how many times will one or more of the clocks go off before they all go off at the same time again?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-6b) Strategy: Make a table or chart Answer: 700 total; 126 red wool, 84 onion rings, 112 cheese

Donald was having a hard time getting to sleep, so he began to count sheep in his imagination. As he watched the sheep jumping over a fence, he noticed that they had a rather unusual appearance. The problem was, he had eaten too much pizza for dinner. For every 9 sheep with tomato-colored wool that Donald counted, 6 sheep had onion rings through their noses, 4 sheep had bell peppers for ears, 12 had mushrooms for eyes, 11 had pepperoni sausages for legs, and 8 were munching on mozzarella cheese. When Donald counted the 56th sheep with bell pepper ears, he got up and took an antacid. How many sheep in all had he counted, and how many of them had red wool, how many had onion rings, and how many were munching on cheese?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-6a) Strategy: Make a table or chart Answer: Viola Voice - 516; Lily Larynx - 672

It is nearing curtain time at the Opera House. The two greatest classical singers in the world, Viola Voice and Lily Larynx, are in their dressing rooms getting ready for their first concert together. Sam, the stage manager, has his hands full receiving flowers from the singers' adoring fans and delivering them to the two prima donnas. At 6:05 he brought 3 bouquets to each singer. At 6:10 he delivered 7 bouquets to Viola and 9 to Lily; five minutes later he delivered 6 bouquets to Viola and 7 to Lily; five minutes later he brought 10 to Viola and 13 to Lily; and five minutes later he delivered 9 to Viola and 11 to Lily. If the flowers keep arriving in this way every five minutes, how many bouquets will each of theopera stars have when the curtain goes up at 8:00?     Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-5f) Strategy: Make an organized list Answer: Trilobat: 13 - 39 oz, Hepplefoot; 14 - 98 oz, Rippersnout; 14 - 406 oz, Fizzlenit; 15 - 570 oz, Fukadoo; 15 - 660 oz

Lenny, the zookeeper's assistant, was exhausted. His new charges were eating up a storm. The tiny-toothed trilobat ate 3 ounces of food at each feeding. When Lenny fed the 3-horned hepplefoot, he had to bring 7 ounces of food, while the red-eyed rippersnout ate 29 ounces at each feeding. The fuzzy-necked fizzlenit ate 38 ounces a feeding and the furry furkadoo ate 44 ounces at a time. After one particularly long day, Lenny made 71 separate feedings, a total of 1,773 ounces of food. How many times did each creature get fed, and how many ounces did each one eat altogether?     Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-5e) Strategy: Make an organized list Answer: Banana yogurt = 216, Bran oatmeal = 156, Chocolate = 270

Andy and Ellen began baking early at the Muffin Mansion, which supplied muffins for local businesses. Today they baked oatmeal bran muffins, which cost $2.31 for one dozen; banana yogurt muffins, which cost $4.52 for one and a half dozen; and chocolate raisin muffins, which cost $7.66 for two and a half dozen. During the breakfast rush they sold a total of 642 muffins for $153.21. How many of each kind of muffin did they sell?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-5d) Strategy: Make an organized list Answer: 72

It happened one day in the towns around Fugit Sound! Television sets started broadcasting the shows they wanted to watch. Radios, stereos, and tape players began playing what they wanted to hear. It was the kind of day science fiction is made of. In one hour, Fred's Repair Shop received 17 calls from owners of sound equipment. Each call was about a radio, a television, a stereo, or a tape player. At least 2 calls came in about each kind of equipment, but the number of calls was different for each kind of equipment. How many different ways could the calls have been divided among the kinds of equipment?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-5c) Strategy: Make an organized list Answer: 66

The community of gnomes in the Magic Forest is upset because their forest is being bulldozed for a shopping mall. The little people are moving far away, too far to walk. They are going in the boats they made from the bark of the trees. Each boat can hold up to and including 100 grams, and still stay afloat. The gnomes, as it happens, come in five different weights: 60 grams (senior citizens), 40 grams (adults), 20 grams (teenagers), 10 grams (children), and 5 grams (infants). What are the possible combinations of gnomes that can safely be put into a boat?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-5b) Strategy: Make an organized list Answer: 54 ways

After waiting in line for hours, Mercedes and her cousin have gotten tickets to the hottest game show on television, "Wheel of Fortune Cookies." The cousins love the part of the game where a contestant spins the wheel four times and after each spin takes a fortune cookie from inside the wheel. Concealed in each fortune cookie is one of these numbers: 0, 1, 6, 7, 9, or 11. The contestant draws out four cookies, and if the total of the numbers inside the cookies is exactly 20, the contestant wins a big prize! How many different ways can a contestant win the big prize?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-5a) Strategy: Make an organized list Answer: 23 apple seeds, 15 peach pits, 28 orange seeds

Everyone knows that Johnny Appleseed went about the countryside planting apple seeds, from which grew beautiful apple trees. But not everyone knows about his two cousins, Penelope Peachpit and Orville Orangeseed, who also planted seeds. In one season these three hard-working cousins all planted industriously. Each of the seeds Johnny planted became an apple tree that yielded exactly 150 apples that season. Each peach pit that Penelope planted became a tree that yielded exactly 275 peaches. Each of the seeds that Orville planted became a tree that yielded exactly 310 oranges. That season, the cousins planted a total of 66 seeds, which yielded a total of 16,255 fruits. How many seeds of each type did the cousins plant?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-4e) Strategy: Look for a pattern Answer: 14^th

Natasha put $10.00 into a savings account at the ltzakick Bank. ltzakick increased Natasha's savings by 100% the second month, then decreased it by 10% the third month. The bank continued to increase Natasha's savings by 100% one month, decrease it by 10% the next, and increase it by 100% the next. In what month will Natasha's savings account grow to $600?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-4d) Strategy: Look for a pattern Answer: 10^th

On Gildan Island there are some amazing amber trees that produce liquid gold instead of sap. Glenda, an islander, has 12 of these trees. The first year, each tree produced 3 gallons of gold. The second year, each tree tripled its production to 9 gallons. Glenda began to keep a record of the liquid gold produced by her trees. The third year, each tree doubled its production to 18 gallons. The fourth year, each tree tripled its output to 54 gallons. The fifth year, each tree doubled its output again. Glenda's record showed a pattern in the way her trees were producing liquid gold: triple output one year, double the next, triple the next, double the next, and so on. If Glenda's trees continue to produce gold at this rate, in what year will her trees produce 125,000 gallons of liquid gold?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S4c) -Strategy: Look for a pattern Answer: Day 10

The king's messengers, out of breath, arrived with terrible news. Penelope, the witch who lived in Black Castle, had cast a spell on the kingdom because the royal photograph developers were too slow! The witch wanted her pictures of the Annual Witch Reunion, and she had been waiting for days. Penelope believed her prints would be particularly handsome. Penelope had declared that each day, until she received her prints, a larger and larger number of the kingdom's subjects would fall asleep. On the first day of the spell 8 subjects fell asleep. On the second day 24 subjects fell asleep - three times as many as the day before. Every day, three times as many subjects fell asleep as on the previous day. On what day would the entire population of 150,000 subjects be asleep, if Penelope continued to wait for her handsome prints?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-4b) Strategy: Look for a pattern Answer: 11

As you may remember, Pinocchio had a rather nasty habit of lying, which caused his nose to grow each time he told a lie. One morning, while working at his father's clock shop, Pinocchio decided to try an experiment. He wanted to see how long he could get his nose to grow. He measured his nose in its natural state and found it was 2 inches long. He shouted, "Cows make the best brain surgeons!" His nose grew 1.5 times longer than the original 2 inches. Now his nose was 5 inches long. "Jellybeans are an excellent source of protein!" he screamed, and again his nose increased 1.5 times the previous amount of growth. His nose was now 9.5 inches long. This is fun, he thought, and yelled, "Chocolate prevents cavities!" If Geppetto's clock shop was 32 feet long, and Pinocchio's nose continued to grow 1.5 times the amount of the previous growth, how many lies did Pinocchio have to tell before his nose reached the opposite wall?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-4a) Strategy: Look for a pattern Answer: 276

Astronomers all over the world are stunned by a remarkable discovery of a new galaxy deep in the farthest reaches of space. This galaxy, which can only be viewed by the most powerful, computerized telescopes, has a unique arrangement. It is composed of many suns, each with its own system of planets revolving around it in a most interesting way. The nearest sun in the new galaxy, called S-1, has just one planet revolving around it. The next closest sun, S-2, has two planets revolving around it. The third sun has three planets, and so on. So far, the information coming back from the new galaxy indicates that there are 23 suns, each farther and farther away from Earth. How many planets are there in the new galaxy?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-3g) Strategy: Use logical reasoning Answer: 8 oak = 13 maple tree

A hotly-debated issue in the enchanted forest is whether to seed the clouds in order to produce more rain. There is a definite difference of opinion among the various types of trees. The forest tree leaders want any vote to be equitable and realize that some types of trees are more numerous than others. The leaders have set up this system: 6 pine tree votes are equal to 9 oak tree votes, 4 beech tree votes are equal to 13 maple tree votes, and 6 beech tree votes are equal to 8 pine tree votes. What would be the balance of maple tree votes to oak tree votes?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-3f) Strategy: Use logical reasoning Answer: 16 lb. Sand; 22 lb fuel

The planets in the Andromedia galaxy are working out a system of trade. The main resource of cold, dark Dox is ice. Hot, dry Sterp has a large quantity of warm sand, which the Doxians need. Aquam, a watery planet with little land, could also use the sand. Torf, which has acres of ancient forests, is a source of fuel for the other planets. So far the planets have worked out this exchange rate: 6 pounds of Doxian ice for 4 pounds of sand from Sterp; 9 pounds of Aquam water for 11 pounds of fuel from Torf; and 6 pounds of Aquam water for 8 pounds of Doxian ice. The residents of Sterp would also like to trade with Torf. Based on the current rates, what would be the exchange rate for fuel and sand?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-3e) Strategy: Use logical reasoning Answer: Locker #1, #4, #9, and #16.

A school has added 20 new lockers to a particular 8^th grade hall.  20 eighth grade students met in the hall and agreed on the following plan:  The first student will proceed down the hall and open all of the lockers.  The second student will then enter the school and close every locker with an even number (2, 4, 6, 8, …).  The third student will then “reverse” every third locker (3, 6, 9, 12, …).  For instance, if a locker is closed, the student will open it; if it is open, the student will close it.  The fourth student will then reverse every fourth locker, and so on until all 20 students have entered the building and reversed the proper lockers.  Which lockers will finally remain open?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-3d) Strategy: Use logical reasoning Answer: 12 children or 6 adults

Gnome-Dome, Inc., is giving thrilling rides in a hot-air balloon. Gnomes from all over the forest are watching the pilot inflate the balloon. The gnomes are eager to climb on board and begin the 60-minute flight. The pilot, however, is concerned about the weight of her passengers. The balloon will only support the weight of 24 gnome-babies. As everyone knows, the weight of 12 baby gnomes is equal to the weight of 4 teenage gnomes; the weight of 6 gnome children is equal to the weight of 3 adults; and the weight of 4 children equals the weight of 8 babies. How many adult gnomes will the balloon support, and how many gnome children will it support?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-3c) Strategy: Use logical reasoning Answer: Luisa--6 blue; Nicolas -- 15 yellow

Luisa and her family are spending the day at Grand America Amusement Park. Each family member has a book of tickets for the rides. Eight gray tickets have the same value as 2 blue tickets, 4 pink tickets have the same value as 3 yellow tickets, and 5 pink tickets have the same value as 6 gray tickets. Luisa and Nicolas really want to go on the Wacky Whirlygig, which costs 24 gray tickets. However, Luisa has only blue tickets left, and her brother Nicolas has only yellow tickets left. How many tickets must each of them use for the Wacky Whirlygig ride?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-3b) Strategy: Use logical reasoning Answer: Jana--laser technician, elsa--bionic engineer, Garth--robot relations, Ian--weather analyst, Hak--shuttle sales, Adriana--robot repairs

Jana, Garth, Ian, EIsa, Hak, and Adriana are all employed in these twenty-first century jobs: bionic engineer, used space shuttle sales, robot repair, intergalactic weather analyst, laser technician, and robot relations counselor. Jana, EIsa, and Adriana did not take robot relations courses in college. The bionic engineer and laser technician often ride the bus with Ian, Hak, and Adriana. The used shuttle salesperson, weather analyst, and bionic engineer often have lunch with Jana, Garth, and Adriana. Hak and the weather analyst work on different floors in the same building. Can you match each person with a job?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-3a) Strategy: Use logical reasoning Answer: 4

A giant brown and white dog named Bernie runs the Mountain Rescue Agency. The agency claims to be ready instantly to handle any rescue mission. Today Bernie is sending Howie on a difficult mission that will take him eight days. Howie can carry food for only five days, so Bernie is looking for volunteers to help Howie reach his destination. Each helper can also carry provisions for only five days. How many dogs need to begin the journey so that Howie will reach his destination?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-2h) Strategy: Work backward Answer: 91

Gary is delivering mail at Twin Towers East. He begins in the morning and takes the elevator to the 17th floor where he leaves 5/6 of his bag and then picks up 22 new letters, memos, and packages. Next stop is the 4th floor to leave 3/7 of his bag, and then pick up 14 pieces of mail. Next he goes to the 30th floor to drop off 1/3 of his bag and then pick up 4 items. Up again to the 43rd floor to deliver 3/4 of his bag and pick up 10 items. Now down to the 10th floor to deliver 1/2 his bag and then collect 2 new items. He then proceeded to the 24th floor to leave 3/5 of his bag. Then he picks up 3 new items. He goes to the 7th floor where he delivers everything he has left - 7 items, and then takes a break. How many pieces of mail did he deliver?  Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-2g) Strategy: Work backward Answer: 60

The monorail at Gateway to the Galaxy delivers people to different rides, and gives them a view of the entire park. Today the first car left the main station with some passengers on board and then stopped at the water rides where it left 1/3 of the people. Then 16 new riders got on. Next stop was the food area where 2/8 of the riders got off. Then 20 new riders got on and rode as far as the roller coaster. Here 12 riders got off before 10 more got on. At the fourth stop 1/4 of the passengers got off and then 3 new ones got on. At the fifth stop 3/8 of the riders got off before 4 new ones got on. At the sixth stop 4 people got off, then 3 new ones got on. At the seventh stop 2/3 of the passengers got off, then 2 new people got on. Finally at the last stop, all 13 of the passengers left got off to hear a concert. How many people got on the monorail in the beginning at the main station?  Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-2f) Strategy: Work backward Answer: 58 dogs

Hector the Collector is dog tired. Every day he sets out early to collect stray dogs before the dog-catcher finds them. During each hour he collects dogs first, and then tries to deliver some to their owners, to make more room in his van. On Tuesday, for instance, during the first hour Hector found a number of dogs but wasn't able to return any. During the second hour he picked up 10 dogs and was able to return 1/2 of the total number he had. In the third hour, he picked up 4 more dogs, and was able to return 1/5 the number that he had. During the fourth hour, he picked up 6, and then returned 1/9 of the total number. In the fifth hour, he picked up 10 and then returned 6. During the sixth hour, he found 2 but wasn't able to return any. In the next hour, he found 14 dogs and was able to return 5/6 of the number he had. During the eighth hour, he didn't find any dogs, but was able to return 4 to their owners. Exhausted, Hector returned home with only 2 dogs. How many dogs did he collect altogether on Tuesday? Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-2e) Strategy: Work backward Answer: 40

Annie has the Saturday delivery schedule for chicken chunks from Rooster-on-the-Run. One Saturday she set out in the truck and left 3/5 of her orders at the college. She went back to the restaurant and picked up 6 orders. Her second delivery was for 3/7 of the total amount that she had in the truck. She headed back to pick up 4 orders and then delivered 3/4 of her total. She picked up 6 more before heading to the local businesses to deliver 1/3 of her orders. She went back for 2 more orders, and delivered 1/2 of her total amount. She returned for 2 orders and made her last delivery of 6 orders at the hospital. How many orders did she deliver altogether?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-2d) Strategy: Work backward Answer: 1500

Bondar came home on the late space shuttle. "Pack your bags," he announced to his six-eyed family members. "We're being transferred to the planet Nebulosa." "Transferred to Nebulosa?" Junior Bondar cried. He ran to his bed chamber and got out a schoolbook. "We're studying Nebulosa in space science," he announced as he opened his book. "Listen to this: Nebulosa has the longest year in the Machinarxian Galaxy. It has 7 seasons. Yam lasts 9% of the year; Creboto lasts 28% of the year; Bevenrob lasts 25% of the year; Tagusa lasts 12.4% of the year; Yanjura lasts 13.8% of the year, and Crembeed lasts 6.6% of the year. Prembeest is 78 days long." Junior Bondar closed the book and sighed. "It's going to be a long wait between birthdays!" How many days will Junior have to wait between birthdays on Nebulosa?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-2c) Strategy: Work backward Answer: Total--1792; mambano--512; plynx--256; stroob--256; mirnk--128; rhynopotamus--128; lulubeak--256; duxter--64; snydeblinker--64; brankomoose--64; dinkelwink--32; shrift--16; (absent--16)

The students at Xynxo Middle School, on the planet Droxnerd, are looking for a new mascot. The student council conducted a poll, asking the students to choose one of the Droxnerdian animals for a mascot. The council found that 2/7 of the student body voted for the three-tailed mambano; 1/7 voted for the pointed plynx; 1/7 voted for the twelve-headed stroob; 1/14 voted for the half-horned rhynopotamus; 1/14 voted for the reversible mirnk; 1/7 voted for the laughing lulubeak; 1/28 voted for the flat-footed duxter; 1/28 voted for the singing snydeblinker; 1/28 voted for the louvered brankomoose; 1/56 voted for the blue-toothed dinkelwink; 1/112 voted for the short-haired shrift; and 16 students were absent. How many students attend Xynxo Middle School, and how many of them voted for each animal?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-2b) Strategy: Work backward Answer: 27

Ramon has a summer job as a bike messenger, delivering packages to businesses and offices downtown. Ramon feels totally cool getting his instructions from the dispatcher over a two-way radio. This morning his first stop was an insurance office where he picked up some packages. His instructions were to drop off 1/2 of those packages at a second building and pick up two more packages. His third stop was a medical building. He dropped off 1/2 of his packages and picked up seven. At his fourth stop, city hall, he dropped off 1/4 of his packages and picked up one. The fifth delivery was to law offices where he left 1/2 of his packages and picked up one. On his sixth stop, Ramon left 6 packages, all that he had left. Then he took a lunch break. How many packages did Ramon deliver before lunch?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-2a) Strategy: Work backward Answer: 400

Asa was reeling after his first day at the Cactus Farm. He would never learn all the plants and their prices! First he sold some tan terps, then twice as many raspberry ribbits as lavender listers, three times as many heavy-footed fungi as pipples, 1.5% more morps than listers, and twice the number of listers as pipples. He sold 26 pipples, which was 6.5% of his total sales for the day. How many cactus plants did Asa sell?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-1d) Strategy: Solve a simpler or a similar problem Answer: won't make it

Jacques, pirate chief of Plunder Island, was slightly diabolical. He left this note for Potter, his partner in crime: "Friday, October 2, 10:00 A.M. I've gone to survey the other side of the island. I will travel 601,920 inches due west. Please meet me there by 5:30 PM. Sharp so we can bury some treasure." Potter found the note 3 hours later. If he left immediately and walked 2 miles an hour, would he make it or was he in big trouble?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-1c) Strategy: Solve a simpler or a similar problem Answer: 760 one pound gold nuggets, 190 three pound gold nuggets, 558 three pound silver nuggets, 186 six pound silver nuggets

Most everyone knows about Ah Baba and the 40 thieves, but not everyone knows about Ah's  younger brother, Bubba Baba. One night Bubba followed Ah and watched him enter the thieves' hideaway. Later, Bubba returned to the hideaway alone and spoke the magic words, "Open Sesame." The door opened and Bubba entered the cave. He was astonished to find 4,120 pounds of gold and silver nuggets. There were four times as many 1-pound gold nuggets as 3-pound gold nuggets. He found three times as many 3-pound silver nuggets as 6-pound silver nuggets. How many gold and silver nuggets of each size did Bubba discover in the thieves' hideaway?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-1b) Strategy: Solve a simpler or a similar problem Answer: Sun. March 25, 12:33 pm

Major Milton Mosquito, commanding officer of the Institute of Invading Insects, is preparing his troops for their first assault of the summer: an annual company picnic on the shores of Lake Oingo-Boingo. "This will be your finest hour," the Major shouts at the troops. "We will meet them at the barbecue pits! We will meet them at the dessert table! We will meet them at the lagoon! We will meet them at the parking lot! It is now 9:00 A.M. Saturday, March 24. Be ready to attack in 99,180 seconds from now." When will the insect invaders first attack the unsuspecting picnickers?    Explain in detail how you found your answer using words, numbers, and/or pictures.

 

8S-1a)Strategy: Solve a simpler or a similar problem Answer: Monday 8:18 pm

Morxian Movie Productions, a studio on the Planet Morx, is searching for someone to play the title role in their upcoming epic "The Creation of the Entire Universe." Starlet Marjorie Minkelmonx read for the part as the universe and the studio executives liked her reading, but unfortunately she weighs only 67 1/2 Morxian pounds. The part calls for someone weighing 879 Morxian pounds. Marjorie has agreed to eat Morxian ice cream non-stop until she weighs enough to play the part. Planet physicians have told her that the ice cream is so rich that she will gain 4 ounces for every minute that she eats it. There are 8 ounces in a Morxian pound, 12 hours in a Morxian day, and 30 minutes in a Morxian hour. Marjorie took her first spoonful of ice cream at 2:15 PM. on Thursday. If she eats ice cream continuously, when will she be ready to step in front of the cameras?    Explain in detail how you found your answer using words, numbers, and/or pictures.