Question

A park ranger spent $208 to buy 12 trees.

Answer 1

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:

$x+y=12...(1)$

$y=12-x...(1)$

We are also told that redwood trees cost $24 each, so cost of x redwood trees would be $24x$.

Each spruce tree costs $16, so cost of y spruce trees would be $16y$.

Since the park ranger spent $208 on trees, so we can represent this information in an equation as:

$24x+16y=208...(2)$

Upon substituting equation (1) in equation (2), we will get:

$24x+16(12-x)=208$

$24x+192-16x=208$

$8x+192=208$

$8x+192-192=208-192$

$8x=16$

$\frac{8x}{8}=\frac{16}{8}$

$x=2$

Therefore, the park ranger bought 2 redwood trees.

Upon substituting $x=2$ in equation (1), we will get:

$y=12-x\Rightarrow 12-2=10$

Therefore, the park ranger bought 10 spruce trees.