Question

There are 850 Douglas fir and Ponderosa pine trees in a section of forest bought by Karamazov Logging Co. The company paid an 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 fir, 500 Ponderosa pine

Explanation:

Let f = the number of fir trees

and p = the number of pine trees.

Then, we have two conditions:

(1) f + p = 850

(2) 300f + 225p = 217 500

(3) p = 850 -f Subtracted f from each side of (1)

(4) 300f + 225(850 - f) = 217 500 Substituted (3) into (3)

300f + 191 250 - 225f = 217 500 Distributed 225

75f + 191 250 = 217 500 Distributed the 7

75f = 26 250 Subtracted 191 250 each side

(5) f = 350

350 + p = 850 Substituted (5) into (1)

p = 500 Subtracted 350 from each side

The company bought 350 fir trees and 500 pine trees.

Check:

(1) 350 + 500 = 850 (2) 300 × 350 + 225 × 500 = 217 500

850 = 850 105 000 + 112 500 = 217 500

217 500 = 217 500

OK.