Question

NEED HELP ASAP!!

Mikes repair shop:
$100 service charge
Plus $65 per hour

Amy’s auto repair shop:
$40 service charge
Plus $80 per hour

Fast forward a few years and suppose you need to get your car repaired. You see the ads above and decide to write an equation to represent the total cost at each repair shop.

X= number of hours for repair
Y= total cost

Mikes repair shop: y=100+65x
Amy’s auto repair: y=40+80x

1. Use the substitution or elimination method to find the point of intersection. SHOW your work below.

2. At what point do the two lines intersect? What is the meaning of the point intersection in the context of this problem?

3. If it takes 3 hours to fix your car, which company is the cheapest and what is the associated cost? SHOW your work below

Answer 1

To find the point of intersection, we can equate the two equations to eliminate either x or y. For example, let's equate them for y:

100 + 65x = 40 + 80x

Solving for x:

60 = 15x

x = 4

Substituting x = 4 into one of the equations, say Mikes repair shop:

y = 100 + 65x

y = 100 + 65 * 4

y = 100 + 260

y = 360

So the point of intersection is (4, 360).

The point of intersection (4, 360) represents the hours and cost at which both repair shops charge the same amount. In other words, if it takes 4 hours to repair your car, then both Mikes repair shop and Amy's auto repair will charge you the same amount of $360.

If it takes 3 hours to fix your car, then the cost at Mikes repair shop will be:

y = 100 + 65x

y = 100 + 65 * 3

y = 100 + 195

y = 295

And the cost at Amy's auto repair will be:

y = 40 + 80x

y = 40 + 80 * 3

y = 40 + 240

y = 280

So Amy's auto repair is cheaper and the cost will be $280.

Hope this helps!