850 douglas fir and ponderosa pine trees in a section of forest bought by a logging company. 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 compnay buy?
Same comment as the previous problem.
To solve this problem, we can set up a system of equations. Let's denote the number of Douglas fir trees as D and the number of ponderosa pine trees as P.
We are given two pieces of information:
1) The total number of trees in the section of the forest is 850: D + P = 850.
2) The company paid a total of $217,500 for the trees: 300D + 225P = 217,500.
We now have a system of two equations with two unknowns. We can solve this system using a method like substitution or elimination to find the values of D and P.
Let's solve by substitution:
1) Solve the first equation for D: D = 850 - P.
2) Substitute this expression for D in the second equation: 300(850 - P) + 225P = 217,500.
3) Distribute and simplify: 255,000 - 300P + 225P = 217,500.
4) Combine like terms: -75P = -37,500.
5) Solve for P: P = (-37,500) / (-75) = 500.
Now substitute the value of P back into the first equation to find D:
D + 500 = 850.
D = 850 - 500 = 350.
Therefore, the logging company bought 350 Douglas fir trees and 500 ponderosa pine trees.