Question

The managers of franks snack shack buys hamburgers in packages of 30 and hamburger buns in packages of 24. He cannot buy part of a pack. What is the least number of packages of each product that he can by to have an equal number of hamburgers buns? How many of each will he have?

Answer 1

He has to buy 4 packages of hamburgers in packages of 30 and 5 packages of hamburgers in packages of 24

Explanation:

First we have to calculate the least common multiple (LCM) of 24 and 30

We will calculate the LCM of 24 and 30 by prime factorization method

24 = 2*2*2*3 =
`2^(3) * 3^(1)`

30 = 2*3*5 =
`2^(1) *3^(1)* 5^(1)`

LCM =
`2^(3)* 3^(1)*5^(1)`

LCM = 120

So number of hamburger buns = 120

Therefore, he must buy 120/24 = 5 packages of hamburgers in packages of 24 and he must also buy 120/30 = 4 packages of hamburgers in packages of 30