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?


First find the additional number of claims John can handle: 30% * 20 claims = 6 claims. Then add that amount to Jan's number of claims to find John's number of claims: 20 claims + 6 claims = 26 claims. Then add the 15 additional claims Missy can handle to find her number: 26 claims + 15 claims = 41 claims.
The answer: 41
Reverse engineering the question: Carla is dividing up insurance claims among 3 agents. Missy can handle 15 more claims than John, who can handle 30% more claims than Jan. If Jan can handle 20 claims, how many claims can Missy handle?


Reasoning and answer: To treat his 20 dogs, Mr. Sean charged Khalil 20 * $60 = $1200. Khalil also paid $40 * 60 = $2400 to Mr. Sean to treat his cats. Altogether, Khalil paid Mr. Sean $2400 + $1200 = $3600 to treat his pets.
The answer: 3600
What was the question?
Question: Mr. Sean has a veterinary clinic where he charges clients $60 to treat a dog and $40 to care for a cat. If Khalil took 20 dogs and 60 cats to the clinic for treatment, how much money did he pay Mr. Sean?


Let x = the number of marbles in the jar. If 50% of the marbles are blue, and 25% of them are red, then the remaining 25% must be either green or yellow. So 0.25 * x = 27 green marbles + 14 yellow marbles = 41 marbles. So there are a total of 4 * 41 = 164 marbles in the jar.
The answer: 164
Reverse engineering the question: A jar full of marbles is sitting on a table. Half of the marbles are blue, a quarter of them are red, 27 of them are green, and 14 of them are yellow. How many marbles are in the jar?


Reasoning and answer: Since the train takes 2 hours longer to go an equal distance as the car, to reach station B, the train took 4.5 + 2 = 6.5 hours. Together, the train and the car take a total of 6.5 + 4.5 = 11 hours to travel from station A to station B.
The answer: 11
What was the question?
Question: A train takes 2 hours longer to go an equal distance of a car. If the car and the train leave station A at the same time, and the car reaches station B 4.5 hours later, calculate the combined time the car and the train take to reach station B.


Reasoning and answer: Kim got 6 points / round x 2 round = 12 points in the easy round. She got 2 points / round x 3 rounds = 6 points in the average round. She got 4 points / round x 5 rounds = 20 points in the difficult round. So her total points is 12 points + 6 points + 20 points = 38 points.
The answer: 38
What was the question?
Question:
The math questions in a contest are divided into three rounds: easy, average, and hard. There are corresponding points given for each round. That is 2, 3, and 5 points for every correct answer in the easy, average, and hard rounds, respectively. Suppose Kim got 6 correct answers in the easy; 2 correct answers in the average; and 4 correct answers in the difficult round, what are her total points in the contest?