Let x represent number of redwood trees and y represent number of spruce trees.
We have been given that a park ranger bought 12 trees. We can represent this information in an equation as:
[tex]x+y=12...(1)[/tex]
[tex]y=12-x...(1)[/tex]
We are also told that redwood trees cost $24 each, so cost of x redwood trees would be [tex]24x[/tex].
Each spruce tree costs $16, so cost of y spruce trees would be [tex]16y[/tex].
Since the park ranger spent $208 on trees, so we can represent this information in an equation as:
[tex]24x+16y=208...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]24x+16(12-x)=208[/tex]
[tex]24x+192-16x=208[/tex]
[tex]8x+192=208[/tex]
[tex]8x+192-192=208-192[/tex]
[tex]8x=16[/tex]
[tex]\frac{8x}{8}=\frac{16}{8}[/tex]
[tex]x=2[/tex]
Therefore, the park ranger bought 2 redwood trees.
Upon substituting [tex]x=2[/tex] in equation (1), we will get:
[tex]y=12-x\Rightarrow 12-2=10[/tex]
Therefore, the park ranger bought 10 spruce trees.
