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Question 1133638: I tried many different ways to do this but could not come with an answer. I put it in my calculator and got the answer, but I wanted to understand the method to getting the answer. I tried to get to the answer in the few ways I tried, but was not successful.
A landscape company is hired to plant trees in three new subdivisions and fixed delivery charge. The company charges the developer for each tree planted, an hourly rate to plant the trees and a fixed delivery charge. In one subdivision it took 166 labor hours to plant 250 trees for a cost of $7520. In a second subdivision, it took 124 labor hours to plant 200 trees for a cost of $5945. In the final subdivision, it took 200 labor hours to plant 300 trees for a cost of $8985. Determine the cost
for each tree, the hourly labor charge and the fixed delivery charge.
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
Let x be the cost of each tree, and let y be the hourly labor cost of planting the trees. The delivery cost is a constant, so call it C. Then the cost equations for the three subdivisions are
(1) 250x+166y+C = 7520
(2) 200x+124y+C = 5945
(3) 300x+200y+C = 8985
The constant difference of 50 trees between the three jobs makes solving the system of equations relatively easy.
Subtracting (2) from (1) gives an equation of the form 50x+??? = ???; and subtracting (1) from (3) gives another equation of the same form. Then subtracting one of those resulting equations from the other eliminates x, allowing you to find the value of y. Then work backwards through your equations to find the values of x and C.
You should find that both the cost per tree and the hourly labor cost are whole numbers of dollars and cents; and that they are reasonable numbers for what they represent.
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