At six years old, with three times as many dogs as cars, Derek had 90 / 3 = 30 cars. Ten years later, after buying 210 more cars, Derek has 210 + 30 = 240 cars. Since the number of cars is twice as many as the number of dogs, Derek currently has 240 / 2 = 120 dogs.
The answer: 120
Reverse engineering the question: Derek was 6 years old when he had three times as many dogs as cars. Ten years later, after selling some of his dogs and buying 210 more cars, the number of cars became twice the number of dogs. How many dogs does Derek have now if he had 90 dogs when he was six years old?


Reasoning and answer: She has 240 minutes to write because 4 x 60 = 240. She will write 2,400 words because 240 x 10 = 2,400. She will earn $240 for the words because 2,400 x .1 = 240. She will earn $180 from the articles because 3 x 60 = 180. She will earn $420 in total because 240 + 180 = 420. She will average $105 an hour because 420 / 4 = 105.
The answer: 105
What was the question?
Question: A reporter is paid by the word and per article. She earns $.1 per word. She earns $60 per article. She has to finish three stories in the next 4 hours. She averages 10 words a minute. How much can she expect to earn per hour if she writes the entire time?


Traveling at 50 yards per minute, Biff can travel 500 yards in 500 / 50 = 10 minutes. In 10 minutes, traveling at 51 yards per minute, Kenneth can travel 10 * 51 = 510 yards. Thus, Kenneth will be 510 - 500 = 10 yards past the finish line when Biff crosses the finish line.
The answer: 10
Reverse engineering the question: Biff and Kenneth decide to compete in a 500-yard rowboat race. If Biff rows at a speed of 50 yards per minute and Kenneth rows at a speed of 51 yards per minute, how many yards past the finish line will Kenneth be when Biff crosses the finish line?


Reasoning and answer: The first has an area of 20 square inches because (4 x 5) = 20. The second has an area of 18 square inches because (3 x 6) = 18. The difference in area is 20 - 18 = 2 square inches.
The answer: 2
What was the question?
Question: Toby has two rectangles of cloth. The first is 4 inches wide and 5 inches tall. The second is 3 inches wide and 6 inches tall. How many more square inches is the area of the first compared to the second?


First find the total volume of the pool: 10 feet * 10 feet * 6 feet = 600 cubic feet. This is also the number of gallons he needs to fill the pool. Subtract the pool water and the drinking and cooking water from the total amount of water Jerry is allowed to use: 1000 gallons - 600 gallons - 100 gallons = 300 gallons. Then divide the amount of water Jerry has left to use for showers by the amount of water per shower to find how many showers he can take: 300 gallons / 20 gallons / shower = 15 showers.
The answer: 15
Reverse engineering the question: Due to a drought, Jerry's household can only use 1000 gallons of water during July. Jerry uses 100 gallons for drinking and cooking and 20 gallons per shower. He wants to fill his pool, which measures 10 feet by 10 feet by 6 feet. If each gallon of water fills 1 cubic foot of the pool, how many showers can Jerry take in July?


If Eugene used all but 16 of the 52 cards, then he used 52 - 16 = 36 cards. If for every card he used 75 toothpicks, then a box of toothpicks would have enough toothpicks for 450 / 75 = 6 cards. Since one box has enough toothpicks for 6 cards, then for 36 cards he would need 36 / 6 = 6 boxes of toothpicks.
The answer: 6
Reverse engineering the question:
Eugene built a model house out of toothpicks and a deck of playing cards. For every card, he used 75 toothpicks. The deck of playing cards had 52 cards, and Eugene used all but 16 of the cards to build his house. If a box of toothpicks contains 450 toothpicks, how many boxes of toothpicks did Eugene use to create his model house?