Question

you have 64 blueberry scones and 72 cranberry scones. you want to make as many identical bags as possible. each bag should have an equal number of blueberry scones and an equal of cranberry scones. what is the greatest number of bags you can fill? SHOW ALL WORK!

Answer 1

8 bags

Explanation:

To find the greatest number of bags you can fill with an equal number of blueberry scones and cranberry scones, you can use the greatest common factor (GCF) of the number of blueberry scones and cranberry scones.

The GCF of 64 and 72 is 8, because 8 is the greatest number that divides evenly into both 64 and 72.

Therefore, you can fill 8 bags with 8 blueberry scones and 8 cranberry scones each, for a total of 8 bags.

To show that this is the maximum number of bags you can fill, you can also divide the number of blueberry scones and cranberry scones by the GCF:

64 scones / 8 = 8 scones/bag

72 scones / 8 = 9 scones/bag

Since the number of blueberry scones and cranberry scones per bag are not equal, you cannot fill any more bags with an equal number of blueberry scones and cranberry scones. Therefore, the greatest number of bags you can fill is 8.