Question

There are 850 Douglas fir and Ponderosa pine trees in a section of forest bought by Karamazov Logging Co. The company paid average of $300 for each Douglas fir and $225 for each Ponderosa pine. If the company paid $217,500 for the trees, how many of each kind did the company buy?

Answer 1

350 Douglas Firs, 500 Ponderosa Pines.

Answer 2

Douglas fir trees are 350 in number and Ponderosa pine trees are 500 in number.

Explanation:

Let the number of Douglas fir be denoted by 'x'

Let the number of Ponderosa pine trees be denoted by 'y'

The company paid average of $300 for each Douglas fir and $225 for each Ponderosa pine.

This gives,
`300x` for total Douglas fir trees and
`225y` for total Ponderosa pine trees.

Total amount paid by the company = 217500

Also given, there are 850 Douglas fir and Ponderosa pine trees which means ;

`x+y=850` or

`x=850-y` ......................(1)

`300x+225y=217500` .............(2)

Putting the value of 'x' from equation 1 into equation 2.

`300(850-y)+225y=217500`

Now, solving this equation we get,

`255000-300y+225y=217500`

`-300y+225y=217500-255000`

`75y=37500`

`y=500`

And we know
`x+y=850`

So, x =
`850-500=350`

Hence, Douglas fir trees are 350 in number and Ponderosa pine trees are 500 in number.