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?
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 is 10.
[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?
[Answer]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 is 41.
Q: 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?
A: 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 is 3600.
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?
Answer: 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 is 164.
[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.
[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 is 11.
[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?
[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 is 38.