Question

In a collection of butterflies there are 4-Monarch butterfly and 12-Swallowtail butterfly. What fraction of the collection is Swallowtail butterflies?

2.Sue and her four sisters are at the Six Flags Amusement Park. They decide to pair up for roller-coaster rides so that each person will ride with each other person. How many rides must be taken?

Answer 1

1. To find the fraction of the collection that is Swallowtail butterflies, we need to divide the number of Swallowtail butterflies by the total number of butterflies in the collection:

Swallowtail butterflies / total butterflies = 12 / (4 + 12) = 12 / 16 = 3 / 4

Therefore, 3/4 of the collection is Swallowtail butterflies.

2. Sue and her four sisters can be paired up in 10 different ways for roller-coaster rides. This is because there are 5 people, and each ride requires 2 people, so we need to calculate the number of combinations of 2 people that can be made from a group of 5:

5 choose 2 = (5 × 4) / (2 × 1) = 10

Therefore, they must take 10 rides to ensure that each person rides with each other person.