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:
![x+y=12...(1)](https://tex.z-dn.net/?f=x%2By%3D12...%281%29)
![y=12-x...(1)](https://tex.z-dn.net/?f=y%3D12-x...%281%29)
We are also told that redwood trees cost $24 each, so cost of x redwood trees would be
.
Each spruce tree costs $16, so cost of y spruce trees would be
.
Since the park ranger spent $208 on trees, so we can represent this information in an equation as:
![24x+16y=208...(2)](https://tex.z-dn.net/?f=24x%2B16y%3D208...%282%29)
Upon substituting equation (1) in equation (2), we will get:
![24x+16(12-x)=208](https://tex.z-dn.net/?f=24x%2B16%2812-x%29%3D208)
![24x+192-16x=208](https://tex.z-dn.net/?f=24x%2B192-16x%3D208)
![8x+192=208](https://tex.z-dn.net/?f=8x%2B192%3D208)
![8x+192-192=208-192](https://tex.z-dn.net/?f=8x%2B192-192%3D208-192)
![8x=16](https://tex.z-dn.net/?f=8x%3D16)
![\frac{8x}{8}=\frac{16}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B8x%7D%7B8%7D%3D%5Cfrac%7B16%7D%7B8%7D)
![x=2](https://tex.z-dn.net/?f=x%3D2)
Therefore, the park ranger bought 2 redwood trees.
Upon substituting
in equation (1), we will get:
![y=12-x\Rightarrow 12-2=10](https://tex.z-dn.net/?f=y%3D12-x%5CRightarrow%2012-2%3D10)
Therefore, the park ranger bought 10 spruce trees.