Let X be the money Jason had at first. Jason spent 1 / 4 * X + 10 on books. Jason spent 2 / 5 * [X - (1 / 4 * X + 10)] + 8 on some DVDs. Jason has X - (1 / 4 * X + 10) - {2 / 5 * [X - (1 / 4 * X + 10)] + 8} = $130 left. X - 1 / 4 * X - 10 - 2 / 5 * X + 1 / 10 * X + 4 - 8 = $130. 9 / 20 * X - 14 = $130. X = $320.
The answer: 320
Reverse engineering the question: Jason spent 1/4 of his money and an additional $10 on some books. He then spent 2/5 of the remaining money and an additional $8 on some DVDs. If he was left with $130, how much money did he have at first?


Reasoning and answer: Each week, Rex is taking 2 hour - long lessons * 2 times a week = 4 lessons. After 6 weeks, he has done 4 lessons per week * 6 weeks = 24 lessons. So Rex still needs 40 total lessons – 24 lessons taken = 16 lessons. He will therefore need lessons for another 16 lessons / 4 lessons per week = 4 weeks.
The answer: 4
What was the question?
Question: Rex is taking lessons for his driver’s license. He wants to take 40 hour-long lessons before his test, and decides to have two-hour sessions twice a week until he has done his test. After 6 weeks, how many more weeks will Rex need to continue taking lessons to reach his goal?


The cassette tapes will cost 2 × 9 = $18. She spends 18 + 25 = $43 in total. Josie will have 50 - 43 = $7 left.
The answer: 7
Reverse engineering the question: Josie received $50 as a gift. She plans to buy two cassette tapes that cost $9 each and a headphone set that costs $25. How much money will she have left?


Reasoning and answer: They had $80 saved up because 2 x 40 = 80. They spent $60 because 80 x (3 / 4) = 60. They had $20 left for ice cream because 80 - 60 = 20. They had $2 left after leaving the ice cream shop because 2 x 1 = 2. They spent $18 on ice cream because 20 - 2 = 18. The bought 12 scoops of ice cream because 18 / 1.5 = 12. The each bought 6 scoops because 12 / 2 = 6.
The answer: 6
What was the question?
Question: Aaron and his brother Carson each saved up $40 to go to dinner. The bill is 3/4 of their total money. After, they go out for ice cream. Each scoop costs $1.5 and they get the same amount as each other. If they leave with $1 in change each, how many scoops did they each buy?


Gabby’s peach tree grew 12 + 1 = 13 peaches. Her plum trees grew 13 * 3 = 39 plums. Thus, Gabby got 1 + 13 + 39 = 53 pieces of fruit to pick.
The answer: 53
Reverse engineering the question: Gabby planted a watermelon vine, a peach tree, and two plum trees in the spring. Over the summer, the plants grew and produced fruit. She only got one watermelon to grow, but she got twelve more peaches than that, and three times that number of plums. How many pieces of fruit did Gabby get to pick that summer?


The company has chopped down a total of 200 + 300 = 500 trees throughout the year. They plant 3 trees for every tree they chop so they need to plant 500 trees * 3 = 1500 trees.
The answer: 1500
Reverse engineering the question:
A paper company decides to operate their business more sustainably. They decide that for every tree they chop down, they want to plant three more. If the company chops down 200 trees in the first half of the year and 300 more trees in the second half of the year, how many more trees does the company need to plant?