[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.
Q: Olaf has an aquarium. He has fish in 3 different colors: orange, green, and blue. Blue fish make up half of all the fish in the aquarium. There are 15 fewer orange fish than blue fish. How many green fish are there when the total number of fish in the aquarium is 80?
A: If there are 80 fish in total, then there are 80 fish / 2 = 40 blue fish. The orange fish count is 15 less than blue, so it's 40 fish - 15 fish = 25 fish. Olaf has then 80 fish - 25 fish - 40 fish = 15 green fish. The answer is 15.
Question: Danny has 3 bottles of soda. He drinks 90% of one bottle and gives 70% of the other two bottles to his friends. How much soda does Danny have left, expressed as a percentage of a bottle?
Answer: First find how much soda Danny drank: 1 bottle * .9 = .9 bottles. Then find how much soda Danny gave to his friends: 2 friends * 1 bottle / friend * .7 = 1.4 bottles. Now subtract the soda drunk and given away to find the remaining amount of soda: 3 bottles - .9 bottles - 1.4 bottles = .7 bottles * 100% = 70%. The answer is 70.
[Question]There are 12 inches to a foot. Blossom measures her room and finds that it is exactly 10 feet long in each direction. In square inches, what is the area of her room?
[Answer]First translate the feet to inches or 10 feet * 12 inches per foot = 120 inches. Then use length * width which is 120 * 120 = 14400 square inches. The answer is 14400.
Q: Mary needs school supplies. She has 6 classes and needs 1 folder for each class. She also needs 3 pencils for each class. She decides that for every 6 pencils she should have 1 eraser. She also needs a set of paints for an art class. Folders cost $6, pencils cost $2, and erasers cost $1. If she spends $80, how much did the set of paints cost in dollars?
A: Mary needs 6 * 1 = 6 folders. Mary needs 6 * 3 = 18 pencils. Mary needs 18 / 6 = 3 erasers. Mary spends 6 * 6 = $36 on folders. Mary spends 18 * 2 = $36 on pencils. Mary spends 3 * 1 = $3 on erasers. Mary spends 36 + 36 + 3 = $75 on all the supplies except the paints. Mary spends 80 - 75 = $5 on the paint set. The answer is 5.
Question: Marcus takes a deck of standard playing cards and takes out all the face cards and the 8's. Mark picks a card at random and then replaces it 36 times. How many times should he expect to pick a card that's both red and has a number divisible by 3?
Answer:
Without the face cards and the 8's, there are 9 cards of each suit. Half these cards are red, and 3 / 9 have numbers divisible by 3, so the odds of drawing a card divisible by 3 are 1 / 3. Multiply the odds of drawing a red card by the odds of drawing a card divisible by 3 to find the odds of both things happening: 1 / 3 * 1 / 2 = 1 / 6. Finally, multiplying the probability of drawing a red / 3 - divisible card by the number of cards Mark draws to find how many he should expect to meet his criteria: 1 / 6 * 36 cards = 6 cards. The answer is 6.