There are 850 Douglass fir and ponderosa pine trees in a sec

There are 850 Douglass fir and ponderosa pine trees in a section of forest bought by Sawz Logging Co. The company paid an average of $300 for 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?

Solution

Let there be X D.Fir trees
Then there are 850-X Pine trees
The Fir trees cost $300 each so total = 300X
The pine trees cost 225 each so total cost = 225(850-X)
Sum total
300X+225(850-X) = 217500
Dividing on both sides with 75
4X+3(850-X) = 2900
4X+2550-3X = 2900
X+2550= 2900
Subtracting 2550 0n both sides
X = 350
which means there are 500 pine trees