Mrs. Danforth packed 5 bags of fun-sized candies for her family's picnic. Each bag contains 16 pieces. She had intended to pass out the same number of candies to each of her 4 children. But Cameron, her second-youngest, argues that she should instead distribute the candies in proportion to the children's ages. All of the children have different ages. If Cameron can convince his mother to give out the candies his way, he will gain two candies while his four-year-old sister will lose twelve. How old is Mrs. Danforth's oldest child?
Here is my attempt at this:
5 bags x 16 candies =80 candies.
80 / 4 = 20 candies per child
Since his 4-year old sister gets 20 -12 =8 candies, then:
8/4 =2 candies per year for each child's age.
Since Cameron will gain 20 + 2 =22 candies, then:
22 / 2 =11 years is Cameron's age.
22 candies of Cameron + 8 candies for youngest sister=30
80 - 30 = 50 candies for the remaining older children.
Since Cameron is the 2nd youngest, it means the remaining 2 siblings must be 12 and 13 years respectively:
So that: 12 x 2 = 24 candies for the 3rd oldest
And 13 x 2 = 26 candies for the oldest child. So, the total distributions of all the candies would be:
8 + 22 + 24 + 26 =80 candies.
So, the oldest child must be 13 years old.