7

Part of 2016 Purple Comet Problems

Problems(2)

Purple Comet 2016 HS Problem 7

Source:

Positive integers m and n are both greater than 50, have a least common multiple equal to 480, and have a greatest common divisor equal to 12. Find m + n.

Purple Comet 2016 MS Problem 7

Source:

4\frac{2}{5}

cups of flour. The recipe for one batch of cookies calls for

1\frac{1}{2}

cups of flour. Melanie plans to make

2\frac{1}{2}

batches of cookies. When she is done, she will have

\frac{m}{n}

cups of flour remaining, where

m

n

are relatively prime positive integers. Find

m + n