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?

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Emmavnichols Emmavnichols · Answer 1 · 2019-03-15T02:16:04+01:00

350 Douglas Firs, 500 Ponderosa Pines.

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chisnau chisnau · Answer 2 · 2019-05-22T08:40:02+02:00

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, [tex]300x[/tex] for total Douglas fir trees and [tex]225y[/tex] 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 ;

[tex]x+y=850[/tex] or

[tex]x=850-y[/tex] ......................(1)

[tex]300x+225y=217500[/tex] .............(2)

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

[tex]300(850-y)+225y=217500[/tex]

Now, solving this equation we get,

[tex]255000-300y+225y=217500[/tex]

[tex]-300y+225y=217500-255000[/tex]

[tex]75y=37500[/tex]

[tex]y=500[/tex]

And we know [tex]x+y=850[/tex]

So, x = [tex]850-500=350[/tex]

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