Mr. Jackson is preparing bags of treats to give trick or treaters on Halloween. He has 48 pieces of candy and 60 pieces of gum. he uses all the candy and gum, and he puts the same ratio of candy to gum in each bag. What is the largest number of bags he could have made?
The GCF is 12.
To find the largest number of bags Mr. Jackson could have made, we need to determine the ratio of candy to gum and then divide the total number of candy and gum by that ratio.
Let's find the ratio of candy to gum:
Candy: 48 pieces
Gum: 60 pieces
To simplify the ratio, we can divide both the candy and gum values by their greatest common divisor (GCD). The GCD of 48 and 60 is 12:
Candy: 48 ÷ 12 = 4
Gum: 60 ÷ 12 = 5
So, the simplified ratio of candy to gum is 4:5.
Now, we can calculate the number of bags by dividing the total number of candy and gum by this ratio:
Total items: 48 + 60 = 108
Bags: 108 ÷ (4 + 5) = 108 ÷ 9 = 12
Therefore, the largest number of bags Mr. Jackson could have made is 12.