SOLUTION: There are 850 Douglas fir and ponderosa pine trees in a section of the forest bought by Sawz Logging Co. The company paid an average of $300 for each Douglas fir and $225 for each

Question 103365: There are 850 Douglas fir and ponderosa pine trees in a section of the forest bought by Sawz Logging Co. 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 company buy?
Answer by ankor@dixie-net.com(12701) (Show Source):
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There are 850 Douglas fir and ponderosa pine trees in a section of the forest bought by Sawz Logging Co. 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 company buy?
:
Let x = no. of fir trees
Let y = no of pine trees
:
It tells us the total is 850 trees, therefore:
x + y = 850
or
y = (850-x); we can use for substitution
:
:
The total value of the trees:
300x + 225y = 217500
:
Substitute (850-x) for y in the above equation, find x:
300x + 225(850-x) = 217500
:
300x + 191250 - 225x = 217500; multiplied what's inside the brackets
:
300x - 225x = 217500 - 191250; subtract 191250 from both sides:
:
75x = 26250
:
x = 26250/75
:
x = 350 fir trees
Then
850 - 350 = 500 pine trees
:
:
Check solution
300(350) + 225(500) =
105000 + 112500 = 217500 as given
:
Not so hard, right?