Q: John decides to go back to school to get his PhD. He first takes 1 year of courses to get acclimated back to school life before starting his PhD. After that, he spends 2 years learning the basics of his field. He then starts research, and he spends 75% more time on research than he did learning the basics. He then spends half as long on writing his dissertation as his acclimation period. How long did it take him to do everything?
A: It took him 2 * .75 = 1.5 years longer to do his research than it took to learn the basics. So it took him a total of 2 + 1.5 = 3.5 years to do research. His dissertation took 1 / 2 = .5 years to write. So everything together took 1 + 2 + 3.5 + .5 = 7 years. The answer is 7.
Question: To keep himself busy in class, Michael makes rubber-band balls. He makes two sizes, large and small. A small ball uses 50 rubber bands. A large ball requires 300 rubber bands. Michael brought a 5,000 pack to class and already made 22 small balls. How many large balls can he make with the remaining rubber bands?
Answer: Michael has used 1,100 rubber bands because 22 x 50 = 1,100. Michael has 3,900 rubber bands remaining because 5,000 - 1,100 = 3,900. Michael can make 13 large balls because 3,900 / 300 = 13. The answer is 13.
[Question]Anna spent 1/4 of her money, and now she has $24 left. How much did she have originally?
[Answer]Let X be the amount Anna had originally. She spent X * 1 / 4 and has X - X * 1 / 4 = $24 left. Combining like terms, we get X * 3 / 4 = $24. Dividing both sides by 3 / 4, we get X = $32. The answer is 32.
Q: A chihuahua, pitbull, and great dane weigh a combined weight of 439 pounds. The pitbull weighs 3 times as much as the chihuahua. The great dane weighs 10 more pounds than triple the pitbull. How much does the great dane weigh?
A: Let x represent the weight of the chihuahua. Pitbull:3x. Great dane:10 + 3(3x) = 10 + 9x. Total:x + 3x + 10 + 9x = 439. 13x + 10 = 439. 13x = 429. x = 33 pounds. Great dane:10 + 9(33) = 307 pounds. The answer is 307.
Question: A boy has 12 oranges. He gives one-third of this number to his brother, one-fourth of the remainder to his friend and keeps the rest for himself. How many does his friend get?
Answer: He gives a third of 12 oranges to his brother which is 12 * (1 / 3) = 4 oranges. He has 12 - 4 = 8 oranges left. He gives a fourth of 8 oranges to his friend which is 8 * (1 / 4) = 2 oranges. The answer is 2.
Q: While preparing balloons for Eva's birthday party, her mom bought 50 balloons and 1800cm of helium. One balloon needs 50cm to float high enough to touch the ceiling, and she can fill any remaining balloon with ordinary air. If she used up all of the helium and inflated every balloon, how many more balloons are touching the ceiling than not?
A:
50cm will make one balloon touch the ceiling so 1800cm will make 1800 / 50 = 36 balloons touch the ceiling. There are 50 balloons in total so 50 - 36 = 14 balloons will not float since they were filled with ordinary air. There are 36 - 14 = 22 more balloons touching the ceiling than not. The answer is 22.