SOLUTION: There are 850 Douglas fir and ponderosa pine trees in a section of forest bought by Sawz Logging Co. The company paid an average of $300 for each Douglas $217,500 for the trees, ho

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Question 67535: There are 850 Douglas fir and ponderosa pine trees in a section of forest bought by Sawz Logging Co. The company paid an average of $300 for each Douglas $217,500 for the trees, how many of each kind did the company buy?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

I BELIEVE THE COST OF OF EACH PONDEROSA WAS ACCIDENTLY OMITTED FROM THIS PROBLEM. IF IT WAS, THEN SUBSTITUTE THAT VALUE INTO THE EQUATION FOR Z.



Let x=number of Douglas Fir
Then 850-x=number of Ponderosa
$300=cost of each Douglas Fir
$Z=cost of each Ponderosa (I BELIEVE THAT THIS VALUE SHOULD HAVE BEEN GIVEN)
We know that Z(850-x)=total cost of the Ponderosa
And $300x=total cost of of the Douglas Fir

Now we are told that the total cost of the ponderosa Z(850-x) plus the total cost of the Douglas Fir 300x equals $217,500. So our equation to solve is:
Z(850-x)+300x=$217,500 clear the parens:
850Z-Zx+300x=$217,500 subtract 850Z from both sides:
300x-Zx=$217,500-850Z
x(300-Z)=217,500-850Z divide both sides by (300-Z)
x=(217,500-850Z)/(300-Z)-------------number of Douglas Fir
850-x equals------------------------number of Ponderosa


Hope this helps----ptaylor