Chapter 8, Problem 6PSP

To determine

To find:

How many hamburgers were eaten?

Answer to Problem 6PSP

19 hamburgers were eaten.

Explanation of Solution

Given:

You are in charge of grilling hamburgers at your class picnic. The hamburgers patties come in packages of 12, and the hamburger buns come in packages of 8. After everyone is finished eating, you have an open package of hamburger patties that contains 5 patties and an open package of hamburger buns that contains 5 buns.

Calculation:

First of all, we will find the least common multiple of 12 and 8 to find the equal number of patties and buns.

Multiples of 8: 8, 16, 24, 32, 40, …

Multiples of 12: 12, 24, 36, 48, …

We can see that 24 is least common multiple of 8 and 12. So you would have purchased 3 packets of hamburgers buns and 2 packages of hamburger patties.

Since you have purchased material for 24 hamburgers, so to find the number of eaten hamburgers, we will subtract 5 from 24 as material for 5 hamburgers was left is packages.

  $\begin{array}{l}\text{Eaten hamburgers}=24-5\\ \text{Eaten hamburgers}=19\end{array}$

Therefore, 19 hamburgers were eaten.