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?
Answers
Let D = # Douglas Firs
Let P = # Ponderosa Pine
equation 1) D + P = 850 there are a total of 850 trees
equation 2) 300D + 225P = 217000 total cost paid
From equation 1 we can solve for either variable in terms of the other.
Let's solve for D in terms of P.
D = 850-P
We can now substitute this value of D into equation 2 to solve for
the number of Ponderosa Pine trees
300(850-P) + 225P = 217000
300(850) - 300P + 225P = 217000
255000 - 75P = 217000
-75P = 217000 - 255000
-75P = -38000
P = (-38000)/(-75)
P = 506 2/3
D = 850-P = 850 - 506 2/3 = 343 1/3
Since we are coming out with fractional answers I assume
the author of this question did not fully check their answers
when they wrote the problem.
Rounding our answers to the nearest whole numbers:
There are 507 Ponderosa Pines and 343 Douglas Firs
Check: 300D + 225P = 217000
300(343) + 225(507) = 217000
102900 + 114075 = 217000
216975 = 217000
As expected, due to the fractional answers which necessitated rounding,
our answer is not exact, but it is certainly as close as we are going to get.