Answer:
- (4, 360)
- cost of repair in either shop is 360 for 4 hours work
- Amy's is cheaper for 3 hours. $280
Explanation:
1.
Each of the given equations describes a line on a graph. There are numerous ways to find the values of x and y that will satisfy both equations at the same time. Two of them you have seen are "substitution" and "elimination." Here, "substitution" is easily accomplished by equating one expression for y to the other expression for y:
y = y
100 +65x = 40 +80x . . . substitute for y
60 +65x = 80x . . . . . . . subtract 40 from both sides
60 = 15x . . . . . . . . . . . . subtract 65x from both sides
4 = x . . . . . . . . . . . . . . divide both sides by 15
y = 40 +80x = 40 +80(4) = 360 . . . . find the value of y
The values of x and y that satisfy both equations are ...
(x, y) = (4, 360)
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2.
The point (4, 360) is on both lines. That is the point where the lines intersect. It means 4 hours work will cost $360 in either shop.
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3.
The time of 4 hours that we found above is the "break-even" or "crossover" point in the cost equations. For times below that point, the lowest cost comes because of the lowest "service charge". For times above that point, the lowest cost comes because of the lowest per-hour charge.
3 hours is less than 4 hours, so the shop with the lowest service charge will have a lower cost. That is Amy's shop. Her price for 3 hours is ...
40 +80(3) = 40 +240 = $280 . . . for 3 hours work in Amy's shop
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If you want to make sure of that, you can find the cost in Mike's shop:
y = 100 +65(3) = 100 +195 = $295 . . . for 3 hours in Mike's shop