Question

The ratio of Monarch butterflies to Queen butterflies at a butterfly farm was 5:2. If there are no additional butterflies at the farm, what is the ratio of Queen butterflies to the total number of butterflies at the farm?

Answer 1

So we know if there are 5 groups/dozens of Monarch butterflies, there are 2 groups/dozens of Queen butterflies. In other words, there are 5 Monarch butterflies for every 2 Queen butterflies.

Then we can turn that into an equation.

$5x = m \\ \\ 2x =q \\ \\ 5x + 2x = m + q$
From the last equation we wrote we can see that the total number of butterflies in the farm is $7x$.

When we compare the Queen butterflies to total butterflies, we get $\frac{q}{m + q} = \frac{2x}{5x + 2x} = \frac{2x}{7x} = \frac{2}{7}$

The ratio of Queen butterflies to total butterflies is 2:7.