850 Douglas fir and ponderosa pine trees in forest boughtpaid an average of $300 for each D fir and $225 for each P pine. (Full prob in description)

Question

Please show in equation form how to solve this story problem. 

 

There are 850 Douglas fir and Ponderosa Pine trees in a section of forest bought by Sawz Logging Co. The company paid $300 for each Douglas Fir and $225 for each Ponderosa Pine. If they paid $217,500 for the whole stand, how many of each type of tree did they buy?

Answer 1

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.