Question

Claire bought 180 pieces of candy and 140 pens to make goodybags for her birthday. What is the greatest number of goodybags Claire can make so that each bag has the same number of pieces of candy and the same number of pens?

Answer 1

Claire can make a maximum of 20 goodybags with equal numbers of candy and pens by finding the greatest common divisor (GCD) of the quantities, which is 20.

Step-by-step explanation:

The subject of this question is Mathematics and the question is suitable for Middle School level. The question asks what is the greatest number of goodybags Claire can make with equal numbers of candy and pens.

To solve this, we need to find the greatest common divisor (GCD) of the number of pieces of candy (180) and pens (140). This GCD will determine the maximum number of goodybags with the same number of items in each. The calculation process is as follows:

1. List the factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
2. List the factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140.
3. Find the common factors between both lists: 1, 2, 4, 5, 10, 20.
4. The greatest common divisor is the largest number in the common factors list, which is 20.

Therefore, the greatest number of goodybags Claire can make so that each bag has the same number of pieces of candy and the same number of pens is 20.