Question

The ratio of North American butterflies to South American butterflies is 5:3. The ratio of South American butterflies to European butterflies is 3:2. There are 30 North American butterflies at the butterfly park. How many South Americans butterflies are there? How many European butterflies are there?

Answer 1

There are 18 South American butterflies and 12 European butterflies.

Explanation:

Let be "s" the number of South American butterflies at the butterfly park.

You know that the ratio of North American butterflies to South American butterflies at a butterfly park is 5:3 and the number of North American butterflies at the butterfly park is 30.

Based on this, you can write the folllowing proportion:

`(5)/(3)=(30)/(s)`

Solving for "s", you get:

`(s)((5)/(3))=30\\\\s=(30)((3)/(5))\\\\s=18`

Let be "e" the number of European butterflies at the butterfly park.

Knowing that the ratio of South American butterflies to European butterflies at the butterfly park is 3:2, and knowing that there are 18 South American butterflies, you can write the following proportion:

`(3)/(2)=(18)/(e)`

Solving for "e", you get:

`(e)((3)/(2))=18\\\\e=(18)((2)/(3))\\\\e=12`