Question 53100: There are 850 Douglas Fir and Ponderosa pine trees in a section of forest. 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 funmath(2933)   (Show Source):
You can put this solution on YOUR website! I answered this for a student yesterday who was told she had to use substitution or elimination to solve it. If you have to do that look back at yesterday's answers. I'm going to show you how to solve this using only one variable, thus avoiding a system of two equations.
Firs+pines=850
Let number of firs=x
Then number of pines:850-x
Cost of firs is 300*number of firs:300x
Cost of pines is 225*number of pines:250(850-x)
Total:217,500
Problem to solve:
300x+225(850-x)=217,500
300x+191,250-225x=217,500
(300-225)x+191,250=217,500
75x+191,250=217,500
75x+191,250-191,250=217,500-191,250
75x=26,250
75x/75=26,250/75
x=350
Number of firs:x=350
Number of pines:850-x=850-350=500
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Check:
300(350)+225(500)=217,500
105,000+112,500=217,500
Seems resonable.
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