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

Answer:

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

Step-by-step 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.  

Answer 2

350 Douglas Firs, 500 Ponderosa Pines.