Question

The ratio of Monarch butterflies to swallowtail in the butterfly garden is 5:3. The ratio of swallowtail to Viceroy is 3:2. There are 30 Monarchs in the park. How many swallowtails are there? Viceroy?

Answer 1

There are 18 swallowtails and 12 viceroy in the butterfly garden.

Step-by-step explanation:

Ratio of monarch to swallowtail = 5:3

Ratio of swallowtail to viceroy = 3:2

Total monarchs = 30

let x be the number of swallowtails.

Using proportion;

Ratio of monarch to swallowtail :: ratio of no. of monarchs to swallowtails

$5:3::30:x$

Product of extreme = Product of mean

$5*x=30*3\\5x=90$

Dividing both sides by 5

$\frac{5x}{5}=\frac{90}{5}\\x=18$

There are 18 swallowtails in the butterfly garden.

Ratio of swallowtail to viceroy = 3:2

let y be the number of viceroy.

Using proportions;

Ratio of swallowtail to viceroy :: Ratio of no. of swallowtail to viceroy

$3:2::18:y$

Product of extreme = Product of mean

$3*y=18*2\\3y=36$

Dividing both sides by 3

$\frac{3y}{3}=\frac{36}{3}\\y=12$

There are 12 viceroy in the butterfly garden.

There are 18 swallowtails and 12 viceroy in the butterfly garden.

Keywords: ratio, proportion

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