Question

PLEASE HELP WITH QUESTION

In January, the ratio of the number of butterflies to the number of bees in a garden was 7 : 3. In February, the butterfly population decreased by 20% while the bee population increased by 30%.
(a) What was the percentage change in the combined butterfly and bee population?
(b) If there were 168 butterflies left in February, what was the butterfly population in January?

Answer 1

a) The percentage change in the combined butterfly and bee population was a decrease of 5%.

b) The butterfly population in January was 210.

Explanation:

In January, the ratio of the number of butterflies to the number of bees in a garden was 7 : 3.

This means that:

`(x)/(y) = (7)/(3)`

In which x is the number of butterflies and y is the number of bees.

In February, the butterfly population decreased by 20% while the bee population increased by 30%.

This means that:

`(x)/(y) = (7*(1-0.2))/(3*(1+0.3)) = (7*0.8)/(3*1.3) = (5.6)/(3.9)`

(a) What was the percentage change in the combined butterfly and bee population?

January: 7 + 3 = 10

February: 5.6 + 3.9 = 9.5

Change

`100*(9.5-10)/(10) = -(50)/(10) = -5`

This means that the percentage change in the combined butterfly and bee population was a decrease of 5%.

(b) If there were 168 butterflies left in February, what was the butterfly population in January?

February is 80% of January, for the population of butterflies. So

`0.8x = 168`

`x = (168)/(0.8)`

`x = 210`

The butterfly population in January was 210.