Andrew M. answered • 10/09/15

Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

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.

Rebecca P.

10/09/15