Question 181361: Problem Solving
13. Jeff clears driveways in the winter to make some extra money. he charges $15/h. Hesketh's Snow Removal charges $150 for the season.
a) Write an equation for the amount Jeff charges to clear a driveway for the season.
b) Write an equation for Hesketh's Snow Removal.
c) What is the intersection point of the two linear equations?
d) In the context of this question, what does the point of intersection represent?
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Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Let y be the total cost of having the snow removed for the season, and x be the number of hours worked by the snow removal crew. Let A be the cost per hour for work done and B be the fixed charges.
Then the equation that gives total cost for the season is:
Jeff charges $15 per hour of work and $0 fixed charges, so Jeff's equation becomes:
Hesketh charges $0 per hour of work and $150 fixed charges, so Hesketh's equation becomes:
The intersection point of the two lines is described by the ordered pair that satisfies both equations, i.e., that value of x that makes y = 150 in Jeff's equation.
That means the point of intersection is described by the ordered pair (10,150)
In the context of the question, the point of intersection illustrates the situation, in terms of number of hours worked by Jeff, that the two services will have the same cost. If you want to bet that it will take less than 10 hours to perform this work over the entire season, hire Jeff. If you think it will take more than 10 hours, hire Hesketh.
John
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