Answer:
a) The percentage change in the combined butterfly and bee population was a decrease of 5%.
b) The butterfly population in January was 210.
Step-by-step explanation:
In January, the ratio of the number of butterflies to the number of bees in a garden was 7 : 3.
This means that:
[tex]\frac{x}{y} = \frac{7}{3}[/tex]
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:
[tex]\frac{x}{y} = \frac{7*(1-0.2)}{3*(1+0.3)} = \frac{7*0.8}{3*1.3} = \frac{5.6}{3.9}[/tex]
(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
[tex]100*\frac{9.5-10}{10} = -\frac{50}{10} = -5[/tex]
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
[tex]0.8x = 168[/tex]
[tex]x = \frac{168}{0.8}[/tex]
[tex]x = 210[/tex]
The butterfly population in January was 210.
