Question

Carlos is making goodie bags for a party. Every goodie bag has exactly the same treats in it. Carlos has 96 granola bars and 64 small popcorn balls. What is the greatest umber of identical goodie bags Carlos can make? How many of each kind of treat is in each goodie bag?

Answer 1

The greatest number of identical goodie bags that Carlos can make is:
`32\ identical\ goodie\ bags`.

`number\ of\ granola\ bars=3\\\\number\ of\ small\ popcorn\ balls=2`

Explanation:

For this exercise you need to find the Greatest Common Factor.

The steps are:

1. Descompose 96 and 64 into their prime factors:

`96=2*2*2*2*2*3=2^5*3\\\\64=2*2*2*2*2*2=2^6`

2. Multiply the commons with the lowest exponent; this will be the GCF.

In this case, this is:

`GCF=2^5\\\\GCF=32`

Therefore, the greatest number of identical goodie bags that Carlos can make is:
`32`.

And the number of each kind of treat is in each goodie bag is:

`number\ of\ granola\ bars=(96)/(32)=3\\\\number\ of\ small\ popcorn\ balls=(64)/(32)=2`