Question

yuko is volunteering at the food bank. He is creating thanksgiving food baskets to give to local families. He has 192 cornbread muffins, 96 cans of vegetables and 64 boxes of stuffing mix. What is the greatest number of baskets yuk can create if he wants to use all of the items and have the same number of each item in each basket? how many of each item will be in a basket?

Answer 1

• 32 baskets
• 2 boxes of stuffing mix, 3 cans of vegetables, 6 cornbread muffins

Explanation:

The greatest common factor (GCF) will be the greatest number of baskets yuko can create. We can examine the factoring of these numbers to see what it might be.

64 = 2^6

96 = 2^5 × 3

192 = 2^6 × 3

The unique factors are 2 and 3, and the lowest powers of each are 5 and 0, respectively. Then the GCF is ...

2^5 × 3^0 = 32 × 1 = 32

After the factor of 32 is removed from each of these numbers, we have ...

64 = 32·2 boxes of stuffing mix

96 = 32·3 cans of vegetables

192 = 32·6 cornbread muffins

These other factors are the numbers of the corresponding item that will be in each of the 32 baskets:

• 2 boxes of stuffing mix
• 3 cans of vegetables
• 6 cornbread muffins