Question

The Leadership Class will be making treat bags for some veterans living at

the Veterans Hospital in Livermore. They have 42 pumpkin cupcakes and
56 glazed donuts to use. What is the greatest number of identical treat
bags that can be made using all the cupcakes and donuts with nothing left
over? What will be in each treat bag?

Answer 1

The greatest number of identical treat bags that can be made is 14, with each bag containing 3 pumpkin cupcakes and 4 glazed donuts, by finding the Greatest Common Divisor of 42 and 56.

Step-by-step explanation:

The question is asking to find the greatest number of identical treat bags that can be made from 42 pumpkin cupcakes and 56 glazed donuts without having any treats left over. The solution to this problem involves finding the Greatest Common Divisor (GCD) of the two numbers.

1. Firstly, list the factors of 42 (1, 2, 3, 6, 7, 14, 21, 42) and 56 (1, 2, 4, 7, 8, 14, 28, 56).
2. Then, identify the largest factor that appears in both lists. In this case, the GCD of 42 and 56 is 14.
3. This means that the greatest number of treat bags that can be made is 14.
4. Since there are 42 cupcakes and 56 donuts, dividing each amount by the GCD (14) gives 3 cupcakes and 4 donuts per treat bag.

Therefore, the Leadership Class can make 14 treat bags, each containing 3 pumpkin cupcakes and 4 glazed donuts.