```Question 73688
Let's begin by identifying the number of Douglas Fir trees as D and the number of Ponderosa Pine
trees as P.
.
The problem tells us that the total number of Douglas Firs and Ponderosa Pines is 850. In
equation form this is:
.
D + P = 850
.
The problem then tells us that for each Douglas Fir the average price paid was \$300. So the
total amount paid for Douglas Firs was 300 dollars times the number of Douglas Firs or 300*D.
.
The problem also tells us that for each Ponderosa Pine the average price paid was \$225.
So the total amount paid for Ponderosa Pines was 225 dollars times the number of Ponderosa Pines
or 225*P.
.
But these two amounts have to add up to be \$217,500. In equation form this becomes:
.
300*D + 225*P = 217500
.
But from our first equation D + P = 850 we can solve for one of the types of trees in
terms of the others.  For example we can solve for D by subtracting P from each side of
this equation to get D = 850 - P.  Knowing this we can substitute 850 - P for D in the second
equation to get:
.
300*(850 - P) + 225*P = 217500
.
Multiply out the left side to get:
.
300*850 - 300*P + 225*P = 217500
.
which reduces to:
.
255000 - 300P + 225P = 217500
.
combine the two terms containing P to get:
.
255000 - 75P = 217500
.
Subtract 255000 from both sides to remove it from the left side.  This subtraction
makes the equation:
.
-75P = -37500
.
You can now solve for P by dividing both sides by -75, the multiplier of P.  When you do
you find that P = 500 trees.
.
But we know that 850 trees were bought.  If 500 of these were Ponderosa Pines, then the
remaining 350 trees had to be Douglas Firs. If you have to show this in equation form you
can start with D + P = 850 and substitute for P the number 500.  This makes the equation:
.
D + 500 = 850
.
Then you just subtract 500 from both sides of the equation to eliminate it from the left
side and when you do you get:
.
D = 350
.
Hope this helps you to identify what you did that was causing you the difficulty.
You got the same 37500 that I did above, but the 75 multiplier on the left side needed to be
divided into that to solve for P.

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