Explain in detail how you found your answer using words, numbers, and/or pictures.      

 8A-31) Answer: 1.4 seconds

A baseball is thrown into the air at 128 feet per second. The ball will be h feet above the ground at t seconds, and h = 128t-16t² . How many seconds after the ball is thrown will it first reach a height of 148 feet? Express your answer as a decimal to the nearest tenth.

Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-30) Answer: 8 apples = 9 pears

Omar is working at the fruit stand after school. One afternoon he decided to get some help with his homework. With the next customer, he made this offer: "If you can correctly solve this riddle, I'll give you 2 pounds of peaches. Six oranges weigh as much as 4 apples. Five bananas weigh the same as 3 pears. Ten bananas weigh the same as 8 oranges. How many pears and apples would you need to have their weights balanced?"    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-29) Answer: 818

BULLETIN: All citizens are asked to be on the lookout for a dangerous animal-like plant that has escaped from the Interplanetary Botany Exhibit. The plant, named Jupiter Tietrap, consumes all kinds of ties: long ties, bow ties, shoe ties, and others. Evidence of the Tietrap's appetite has already been seen at four shops in Mars Park Plaza. There are 26 ties missing from the first shop, 38 from the second shop, 62 from the third shop, and 98 from the fourth shop. The increase in ties taken is always 12 more than the previous increase. If the Tietrap continues to eat ties at that rate, how many ties will it devour in the 12th shop?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-28) Answer: 37 years old

Exotic plant life covers the planet Botone in the distant galaxy of Hydroxia. One of the strangest of trees on the planet produces a delicious fruit with a creamy texture and a chocolate flavor. Every year the tree produces one more pound of the fruit than the previous year. In the first year it produced one pound, in the second year two pounds, in the third year three pounds, and so on. This year was the first time that one tree bore over 700 pounds of the wonderful fruit. How many years old is that tree?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-27) Answer: Day 61

The town is buzzing with the news: The Teah has returned! Everyone groans. The Teah is a water monster with an enormous thirst. It slips unseen into the favorite lake of the townsfolk and begins its work. On its first day in residence, it politely drinks only one gallon of water The second day, it drinks two gallons. The third day, it consumes three gallons. The summer goes on and the Teah keeps drinking until it has consumed 1,830 gallons of water. The next day it slips away as quietly as it came. On what day did the Teah leave the lake?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-26) Answer: 108

Brenda Beetle and Marcia Mosquito followed the trail to other bugs to the Registration Center of Ivy Leaf High School. Brenda and Marcia felt frightened by the large number of bugs at the center, but they did their best to encourage one another. Brenda whispered nervously, "How many bugs do you think there are here?" Marcia, trying to take Brenda's mind off her fears, said, "Take 97 of the total number of bugs, double it, and you wilI have 6 more than 1 1/2 times the number of bugs in this crowd." How many bugs were at the Ivy Leaf Registration Center?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-25) Answer: $7,260.50

"Look," complained Trixie Troll. "I'm getting tired of hanging out under the bridge and shouting 'Trip-trap, trip-trap, who is tripping on my bridge?' a zillion times a day. I've been doing it for centuries, and enough is enough! Let's build tollbooths on our bridges. We'll post the tolls and have no more fairy tale nonsense about it!" Trixie's sister, Trina, and her brothers, Troy and Trevor, agreed. Each Troll took charge of a separate bridge and built his or her own toll booth. Troy charged $.64 toll; Trina made each traveler pay $5; Trixie set her toll at $1.25; Trevor charged $2.10. During the first month, Troy collected tolls from 700 travelers; Trina collected from 473 travelers; Trixie collected tolls from half as many travelers as Troy did; and Trevor collected tolls from three times as many travelers as Troy did. After they paid taxes to the bridge commissioner, each of the four trolls had $100.00 profit. How much tax did the trolls pay together?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-24) Answer: 27 days

Serena, locked in a castle dungeon, is digging her way to freedom. On the other side of the castle wall, her sister Stephanie is also digging. It is a distance of 30 feet from Serena's cell to Stephanie. Sometimes they dig a few feet, only to lose ground because of the walls falling in. On the first day Stephanie digs 3 feet and Serena 2 feet. At the end of the second day both Serena and Stephanie have tunnels only 1 foot long. On the third day Serena has a tunnel 3 feet long, and Stephanie 4 feet. On the fourth day, Serena's tunnel is 2 feet and Stephanie's 2 feet. On the fifth day, Serena has gone 4 feet and Stephanie 5 feet. If they keep constructing their tunnels at this rate, how many days will it be when Serena can escape?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-23) Answer: 324

Gina and some friends are gathering information for a paper on astrological signs. For the 477 classmates born under Virgo, Gemini, Leo, Pisces, and Aquarius, they discovered that there were six times as many Virgos as Geminis; 3/8 as many Leos as Virgos; 1/2 as many Pisces as the combined total of Leos and Virgos; and 5 more than 1/3 the number of Pisces were Aquarius. How many of the 477 classmates were born under Virgo and Pisces?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-22) Answer: 30^th

Ticket lines are huge around the Colossal Arena. The Boulders, one of the most popular rock groups ever, are giving a concert on Saturday. When the tickets went on sale Monday, 500 were sold in the first hour, 560 tickets were sold in the second hour, and 640 tickets were sold in the third hour. After the second hour, the increase in ticket sales every hour was 20 more than the increase of the previous hour. If sales continue at that rate, in what hour will 10,000 tickets be sold for the Boulders concert?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-21) Answer: 14^th

Dr. A. B. Loney is a marine biologist charting the number of sharks, whales, jellyfish, and stingrays found in the Pacific Ocean. On the first day he found 7 sharks, 3 whales, 2 jellyfish, and 4 stingrays. The second day he counted 6 sharks, 5 whales, 8 jellyfish, and 8 stingrays. On the third day he counted 8 sharks, 4 whales, 5 jellyfish, and 7 stingrays. The fourth day he counted 7 sharks, 6 whales, 11 jellyfish, and 11 stingrays; and on the fifth day 9 sharks, 5 whales, 8 jellyfish, and 10 stingrays. If he continues to spot the animals at the same rates, on what day will he spot 75 animals?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-20) Answer: 150 octopi, 106 nonopi, 121 decapi

Everyone knows that octopi have 8 tentacles. But the only human being on earth who knows that there are other kinds of octopi is a watch salesman named Irving. Every five years Irving hires a diving bell and goes to the bottom of the sea, where there is a community of octopi, nonopi (with 9 tentacles), and decapi (with 10 tentacles). Irving sells waterproof watches for several days. He knows that the total population of the three types of creatures is 377. In order for each creature to wear a watch on each tentacle, Irving will have to bring 3,364 watches. How many of the creatures are octopi, how many are nonopi, and how many are decapi?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-19) Answer: 168 oz cactus root = 10-8 oz dried spiders

Anastasia of the Magic Forest is a bit absent-minded. Once a week she makes a batch of magic potion. But every week she seems to be out of something that she needs for her recipe, so she has to refer to her chart of equivalencies and try to substitute as best she can. Her chart lists these equivalencies: 7 ounces of powdered snail shell may be substituted for 12 ounces of dried spider; 3 ounces of bats' wings may be substituted for 5 ounces of frog toes; and 24 ounces of cactus root may be substituted for 9 ounces of powdered snail shell. Today she is fresh out of powdered snail shell and dried spider. What can she substitute for dried spider and in what amount?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-18) Answer: Milo 27, mother 54, grandfather 72

Milo's age is the same as his grandfather's with the digits reversed. The product of their ages gives a year during World War II. If Milo's mother is twice as old as Milo, then how old is Milo, his mother, and his grandfather?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-17) Answer: 703

It is a little-known fact that when Snow White first arrived at the home of the dwarfs, there were actually 37 of the little fellows in residence-far too many for her to remember their names. So Snow numbered them, Dwarf #1 through Dwarf #37, and that helped. She had been there only a day or so when the dwarfs asked her if she would mind making sandwiches for their lunches at the mines. Thirty-seven sandwiches seemed like a lot to Snow, but the rent was free, so she agreed. She had just whipped out her butter knife when the dwarf with the big nose announced that 37 sandwiches would not be enough. It seems that Dwarf #1 ate one sandwich, Dwarf #2 ate two sandwiches, Dwarf #3 ate three sandwiches, and so on. Snow turned white. "You have GOT to be kidding!" she gasped. She began packing her bags, figuring that she would rather take her chances with the Queen. Then Dwarfs #8 through #37 revealed that they would be moving out the next day, so would Snow mind making all those sandwiches just for one day? Snow agreed and everyone lived happily ever after. How many sandwiches did Snow make for all 37 dwarfs that day?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-16) Answer: 1215 total; 390 monarch; 210 tiger swallowtail; 510 painted lady; 105 fritillary

Princess Rosalinda is to be married next week. The royal bakers have been working around the clock for a week, preparing the cakes for the wedding. Since the princess loves butterflies, each cake will be decorated with a butterfly made of icing. For every 26 cakes decorated with monarch butterflies, 14 cakes will be decorated with tiger swallowtails, 34 will be decorated with painted ladies, and 7 will be decorated with fritillary butterflies. The royal bakers already have 390 cakes decorated with monarch butterflies. How many cakes have they made in all, and how many cakes are there with each kind of decoration on them?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-15) Answer: Betelgeuse - $15,000; Rigel - $18,750; Arcturas - $37,500; Sirius - $56,250

"Twinkle Twinkle Little Star," sing the Earthlings, not knowing that starbops deliver 510,000 dars of fuel per hour to Sirius, Arcturus, Rigel, and Betelgeuse. The brighter the star, the more fuel is needed to keep it shining. Starbops deliver 1.5 times as much fuel to Sirius as to Arcturus, and 2 times as much fuel to Arcturus as to Rigel. They carry 1.25 times as much fuel to Rigel as to Betelgeuse. The cost of one dar of star fuel is $15. What is the cost per minute for fueling each star?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-14) Answer: 16 Combos, 17 Hot dogs, 22 Hamburgers, 25 Sodas

Lance and Mario were working in the snack bar at the Turbulent Tunas Concert. They sold hot dogs for $1.65, hamburgers for $2.35, sodas for $.85, and the combo plate with fries, salad, a hamburger; and soda for $3.89. They sold 80 items in an hour for $163.24. How many of each kind of food did they sell, and how much did they make on each kind of food?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-13) Answer: 8 days

Rats had always been a problem in the little town of Hamlin, but when the mayor found nibbles out of his favorite cheese, he knew enough was enough! Since the exterminator was on vacation, the mayor sent out a plea for help. A flute player with the municipal orchestra volunteered his assistance. "By doing what?" asked the mayor. "By playing my flute," the flutist responded, and he played for the mayor who was very impressed. The mayor agreed to let the piper try to lure the rats out of town by playing his flute. There were 1500 rats in the town of Hamlin. On the first day of tooting, 10% of the rats followed the flutist out of town and into the sea. Each day 10% more rats left town than had left the previous day. At this rate, what day would be the final day that the flutist would have to toot?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-12) Answer: $3,769

Remember the old woman who lived in a shoe and had so many children she didn't know what to do? Well, a freeway was built right next to the shoe, so she and the children opened shop at the off-ramp. The children made lawn ornaments, sugar bowls, hats, and sunglasses-all looking like pink flamingos. The first week they made 4 lawn ornaments, 9 sugar bowls, 3 hats, and 2 pairs of sunglasses. The second week they made 8 lawn ornaments, 16 sugar bowls, 9 hats, and 8 pairs of sunglasses. The next week they made 7 lawn ornaments, 17 sugar bowls, 6 hats, and 7 pairs of sunglasses. The fourth week they made 14 lawn ornaments, 24 sugar bowls, 18 hats, and 13 pairs of sunglasses. The next week they made 13 lawn ornaments, 25 sugar bowls, 15 hats, and 12 pairs of sunglasses. If the children continue to make the products at that rate, and the woman sells the items at $1.00 each, how much money will they make-the 15th week?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-11) Answer: 9 days

Neville Newt said, "Generally I like rain, but this is ridiculous. If this continues, we'll have to get the beavers to build an ark!" During the first storm, they got .5 inches of rain. Each day after that, they got 50% more rain than on the previous day. At that rate, how long would it be before they had 25 inches of rain?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-10) Answer: 6 Yorx $, 75 Greenbe $

The first interstellar tourist shuttle is ready for departure to the planets Zerbo, Yorx, Greebe, and Blinko. Tourists from all over Earth are waiting to board. They are eager to shop in the stores on the different planets. As they shop they will have to remember that 9 Zerbo dollars have the same value as 3 Yorx dollars; 6 Blinko dollars have the same value as 5 Greebe dollars; and 10 Blinko dollars have the same value as 2 Zerbo dollars. A solar-powered dog polisher on Blinko costs 90 Blinko dollars. How much would it cost in Yorx dollars and in Greebe dollars?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-9) Answer: Diamond City - 20; Heart City - 21; Club City - 16

Allison Wonderland and her family were vacationing in a very peculiar city. Everyone in the city spoke in equations. Mr. Wonderland pulled into a gas station and asked the attendant how many miles they were from Diamond City, Heart City, and Club City. The attendant, a strange-looking man in a tall hat, pointed north and said, "2/5 of the number of miles to Diamond City, plus 32, is equal to 2 times the number of miles to Diamond City." Then he pointed south and said, "1/3 the number of miles to Heart City, plus 35, is equal to 2 times the number of miles to Heart City." Then he poured himself some tea, and pointed to the east and said, "1/2 the number of miles to Club City, plus 40, is equal to 3 times the number of miles to Club City." As they left the gas station, Mrs. Wonderland pulled out her calculator, but Allison said they didn't need it. How far were they from each city?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-8) Answer: 39

It is the Tenth Anniversary of the opening of Grand America Amusement Park. In celebration of the event, the park is giving away free passes for five minutes after the gates open. The first person through the gate will receive one free pass, the second person will receive two free passes, the third will receive three, and so on. Hirotomo wants very much to get enough free passes for everyone in his church, which means he will need 820 passes. If Hirotomo is first in line and gets others from his group to stand in line behind him, how many others will he need to help him in order to get enough tickets for the whole church?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-7) Answer: 500 magic kits, boxes, cards

At Now You See It, Now You Don't, Jill sold magic kits to aspiring magicians. Last week she sold a lot of card tricks; 20.6% more rope tricks than rabbits-in-a-hat kits; 1/3 as many mice-in-the-pocket kits as the rabbit kits; 10 times as many rabbit kits as trick boxes; twice as many disappearing-dollar tricks as trick boxes; and 9 trick boxes. The boxes were 1.8% of the total number of items that she sold. How many magic kits, trick boxes, and card tricks did Jill sell?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-6) Answer: 329

A recent survey at the Tummy Yummies Dog Food Company revealed that for every package of Beef Stew sold, doggie diners devoured 7 packages of Mellow Meatloaf, 6 packages of Chopped Chicken Chow Mein, and 9 packages of Barbequed Beef. They discovered that for every 2 packages of Beef Stew sold, one package of Mush Mix was purchased. If Tummy Yummies Dog Food Company sold 84 packages of chicken dinners one day, how many dinners did they sell altogether?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-5) Answer: 10^th

On Grand Opening Day, Toofer's Tape Store opened at 8:00 AM. In the first hour Tom Toofer sold 4 tapes. In the second hour he sold 8 tapes, twice as many as in the first hour. In the third hour, customers bought 16 tapes, twice as many as the previous hour. In the next hour Tom sold three-fourths as many as in the previous hour, or 12 tapes. Tom kept selling tapes in the same way all morning: twice as many as the previous hour, twice as many as the previous hour, then three-fourths as many as the previous hour. And Tom gave customers one free tape for every tape they bought. During the last hour Toofer's was open, customers left the store with 1,296 tapes. How late did the store stay open?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-4) Answer: 39 sea animals

Claude kept track of what he saw at Sea Universe Theme Park. He saw twice as many sharks as dolphins. The number of whales was 6 less than the number of sharks. There were 5 times as many sea lions as there were whales. He saw 20 sea lions. How many did he see altogether?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-3) Answer: hammer $4; pliers $2

In Zolt's Hardware Store, you can buy homeowners' tools in savings packs. In the Basic-Pak, you get a hammer, a pair of pliers, and a screwdriver for $7.50. In the Starter-Pak, you get two hammers, two pairs of pliers, and four screwdrivers for $18.00. In the Family-Pak, you get five hammers and four pairs of pliers for $28.00. How much do each of the tools cost?    Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-2) Answer: 20%

Mrs. Ross has 55 percent of the senior class students in her Advanced Physics class. Mr. Luellan has 35 percent of the senior class in his Calculus class. 10 percent of the senior class is taking both classes. What percent of the senior class is taking neither of these classes?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8A-1)  Answer: 12 grandchildren

A gentleman gave 4 cents each to his little grandchildren; had he given them 7 cents each, it would have taken 36 cents more; how many little grandchildren did he have?    Explain in detail how you found your answer using words, numbers, and/or pictures.

Share a problem (thank you) to add to this list and submit to:   donna_buck@pasd.wednet.edu Please title the subject "Problems for 8A" and include the answer.