Answer:
1. Point of intersection = (4, 360)
2. (4, 360) number of hours and the total cost of the repairs is the same for both repair shops
3. Amy's Auto Repair: $280
Step-by-step explanation:
1. y = 100 + 65x and y = 40 + 80x
Equate the equations and solve for x:
y = y ⇒ 100 + 65x = 40 + 80x
subtract 65x from both sides ⇒ 100 = 40 + 15x
subtract 40 from both sides ⇒ 60 = 15x
divide both sides by 15 ⇒ 4 = x
Therefore, x = 4
Substitute x = 4 into either of the equations to find y:
⇒ y = 40 + (80 x 4) = 40 + 320 = 360
Point of intersection = (4, 360)
2. The two lines intersect at (4, 360)
In this context, the point of intersection is where the number of hours and the total cost of the repairs is the same for both repair shops.
3. Substitute x = 3 into the equations and compare:
Mike's repair shop: y = 100 + (65 x 3) = 295
Amy's auto repair: y = 40 + (80 x 3) = 280
Therefore, Amy's Auto Repair is the cheapest (as 280 < 295) and the cost is $280.
