Question

The ratio of North American butterflies to South American butterflies at a butterfly park 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 European butterflies are there?

Answer 1

Answer: There are 12 European butterflies.

Step-by-step explanation:

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

Since 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, you can write the folllowing proportion:

$\frac{5}{3}=\frac{30}{s}$

Solving for "s", you get:

$(s)(\frac{5}{3})=30\\\\s=(30)(\frac{3}{5})\\\\s=18$

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 since there are 18 South American butterflies, you can write the following proportion:

$\frac{3}{2}=\frac{18}{e}$

Solving for "e", you get:

$(e)(\frac{3}{2})=18\\\\e=(18)(\frac{2}{3})\\\\e=12$