The ratio of North American Butterflies to South American butterflies at a butterfly park is 7:5. The ratio of South American butterflies to European butterflies is 5:3. There are 105 North American butterflies at the butterfly park.

Question

How many South American butterflies are there?

Answer 1

NA butterflies : SA butterflies = 7:5
SA butterflies : E butterflies = 5:3

so
NA : SA : E = 7 : 5 : 3 = 7x : 5x : 3x

given: 7x = 105
x = 15
So SA butterflies = 5x = 75

SA butterflies was the link between the two ratios, luckily the terms of the ratios were the same
If not, we would have had to find a common term, (similar to finding a LCD)