John received twice as many points as Hunter, who received a 45 so John scored 2 * 45 = 90 on his test. Grants scored 10 more points than John who got a 90 so Grant received 10 + 90 = 100 on his test.
The answer: 100
Reverse engineering the question: Grant scored 10 points higher on his math test than John. John received twice as many points as Hunter who scored a 45 on his math test. What was Grant's test score?
Reasoning and answer: In 2005, 60 / 2 = 30 kids came to the cookout. In 2006, 30 / 3 * 2 = 20 kids came to the cookout.
The answer: 20
What was the question?
Question: In 2004, there were 60 kids at a cookout. In 2005, half the number of kids came to the cookout as compared to 2004. In 2006, 2/3 as many kids came to the cookout as in 2005. How many kids came to the cookout in 2006?
Let a be the amount of time Maryann spends doing accounting and c be the amount of time she spends calling clients: We know that a + c = 560 and a = 7c. Substituting the second equation into the first equation, we get 7c + c = 560. Combining like terms, we get 8c = 560. Dividing both sides by 8, we get c = 70.
The answer: 70
Reverse engineering the question: Maryann spends seven times as long doing accounting as calling clients. If she worked 560 minutes today, how many minutes did she spend calling clients?
Reasoning and answer: In the large orders, Lisa used 3 large orders * 200g of packing peanuts per large order = 600g of packing peanuts. The rest of the packing peanuts were used in small orders so there was a total of 800g packing peanuts - 600g of packing peanuts used in large orders = 200g of packing peanuts used in small orders. So there must have been 200g of packing peanuts / 50g of packing peanuts per small order = 4 small orders.
The answer: 4
What was the question?
Question: Vanessa's new business is thriving and she frequently has orders to post. She has run out of packing peanuts for the packages and is now wondering how many orders she has sent. Each large order needs 200g of packing peanuts while small orders need just 50g of packing peanuts. If Lisa has used a total of 800g of packing peanuts and she knows she has sent 3 large orders, how many small orders has Lisa sent?
The total marks for the first ten students are 90 * 10 = 900 marks. The 15 students who scored ten marks fewer than the first ten had 90 - 10 = 80 marks each. The total marks for the following 15 students are 15 * 80 = 1200 marks. The total number of students who scored above sixty is 10 + 15 = 25. If 50 students were present in the class, those who scored sixty are 50 - 25 = 25. If 25 students scored 60, then their total marks are 60 * 25 = 1500 marks. The whole class scored a total of 1500 + 1200 + 900 = 3600 marks. The average for the class is 3600 / 50 = 72 marks.
The answer: 72
Reverse engineering the question: The number of students in Kylie's class is 50. In a particular test, ten students scored 90 marks, 15 scored ten marks fewer than the first ten students, and the rest scored 60 marks each. What are the average marks for the whole class?
The third and fourth day contributed 6 + 18 = 24 inches to the depth of the snowdrift. Therefore, the size of the snowdrift after half was melted on the second day, but before the snowfall on the third and fourth day, was 34 - 24 = 10 inches. If the size of the drift on the second day, after half of the snow had melted, was 10 inches, then the depth of the original drift created on day 1 was 2 * 10 = 20 inches deep.
The answer: 20
Reverse engineering the question:
A big snowstorm caused a large amount of snow to fall onto Grandpa's farm, and the wind caused the snow to pile up into a drift. But on the second day, it warmed up enough that half of the snowdrift melted. The third day, it snowed again, adding another 6 inches of snow onto the snowdrift. On the fourth day, another 18 inches of snow fell onto the snowdrift. If the snowdrift was 34 inches deep at the end of the fourth day, how deep in inches was the drift at the end of the first day?