Reasoning and answer: Let b be Bill's years of experience and j be Joan's years of experience. We know that j - 5 = 3(b - 5) and j = 2b. Substituting the second equation into the first equation, we get 2b - 5 = 3(b - 5). Multiplying through the parentheses, we get 2b - 5 = 3b - 15. Adding 15 to both sides, we get 2b + 10 = 3b. Subtracting 2b from both sides, we get 10 = b.
The answer: 10
What was the question?
Question: Bill and Joan both work for a library. 5 years ago, Joan had 3 times as much experience as Bill. Now she has twice as much experience as Bill. How many years of experience does Bill have now?
Each year Tony has one more fish than before because 2 - 1 = 1. In five years, he will have 5 more fish because 5 x 1 = 5. In five years he will have 7 fish because 2 + 5 = 7.
The answer: 7
Reverse engineering the question: Tony has two fish. Every year, his parents buy him two more, but one of them dies. How many fish will he have in five years?
Reasoning and answer: He runs at .1 miles per minute because 6 / 60 = .1. While the album is playing he can run 4 miles because 40 x .1 = 4. He has to run 2 miles without the album because 6 - 4 = 2. Without music he runs 1 / 15 miles per minute because 4 / 60 = 1 / 15. He will run the remaining 2 miles in 30 minutes because 2 / (1 / 15) = 30. It will take him 70 minutes in total because 40 + 30 = 70.
The answer: 70
What was the question?
Question: Charles is jogging while listening to his favorite album. He runs at 6 MPH when he's got music on and 4 MPH when he doesn't. His album is 40 minutes long. How many minutes will it take him to jog 6 miles?
20 of 50 marbles are white so there are 50 - 20 = 30 red and blue marbles. The number of red marbles and blue marbles is the same, so there are 30 / 2 = 15 of each color. The difference between the number of white marbles and blue marbles is 20 - 15 = 5. Double the difference is 5 * 2 = 10 marbles. 10 marbles are removed to leave 50 - 10 = 40 marbles.
The answer: 40
Reverse engineering the question: There are 50 marbles in a box which has a mixture of white, red and blue marbles. There were originally 20 white marbles and an equal number of red and blue marbles. Jack removes a number of marbles equal to double the difference between the number of white marbles and the number of blue marbles. How many marbles are left in the box?
Reasoning and answer: After losing one of the pages you have 12 - 1 = 11 pages of stickers. If each page has 20 stickers on it, you have 11 x 20 = 220 stickers.
The answer: 220
What was the question?
Question: There are 20 stickers on a page. If you have 12 pages of stickers but lose one of the pages, then how many stickers would you have?
Reasoning and answer: The ratio between the time charged and the time to be charged is 100 / 25 = 4. To reach 100%, the cell must be charged for 45 minutes * 4 = 180 minutes. Subtracting the 45 minutes that Jimmy already used to charge the cell phone, there are still 180 - 45 = 135 minutes of charging time left.
The answer: 135
What was the question?
Question:
Nick's cell phone was initially empty but was then charged for 45 minutes and has reached a 25% charge. How much longer must the cell phone be charged to reach 100% charge?