Final answer:
To create party bags with an equal amount of candies, we could use 1 Jolly Rancher and 1 chocolate bar per bag, resulting in 8 bags with Sean's candies all used up and Ruth having 10 chocolate bars left over.
Step-by-step explanation:
The question involves determining how many Jolly Ranchers and chocolate bars need to be in each party bag to ensure that both include an equal amount. Sean has 8 Jolly Ranchers and Ruth has 18 chocolate bars. To make bags with equal amounts of each, we can find the greatest common divisor (GCD) of 8 and 18, which will tell us the largest number of items per bag possible for both types of candy while keeping the counts equal.
The GCD of 8 and 18 is 2. This means that each party bag could have 2 Jolly Ranchers and 2 chocolate bars. However, we can easily see that we cannot use all of the candies as 2 does not divide into 18 evenly. Since there is no higher number that divides into both 8 and 18, we have to use the next best option, which is 1 candy per bag. So each party bag would have 1 Jolly Rancher and 1 chocolate bar, and we would make 8 bags in total because Sean only has 8 Jolly Ranchers. This will leave Ruth with 10 leftover chocolate bars.