Question

A park ranger spent $208 to buy 12 trees.

Redwood trees cost $24 each and
spruce trees cost $16 each. How many of
each tree did the park ranger buy?

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`

`(8x)/(8)=(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.