Question

WILL GIVE BRAINLIEST

MIKE’S REPAIR SHOP
$100 Service Charge
plus $65 per hour


AMY’S AUTO REPAIR
$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. Your father, who knows a bit about
cars, says it will probably take 3 hours to fix your car. How do you
determine where you should take your car to get it repaired?
1. Write an equation for each repair shop to represent the total cost of the car

repair as a function of the number of hours worked.

Let x = number of hours worked Let y = total cost to you

Mike’s Repair Shop _______________________________________

Amy’s Auto Repair ________________________________________

2. Now, use the substitution or elimination method to find the point of

intersection. Show your work below:

Auto Repair Problem

“Which auto repair service should I use?”

MIKE’S REPAIR SHOP

$100 Service Charge

plus $65 per hour

AMY’S AUTO REPAIR

$40 Service Charge

plus $80 per hour

3. At what point do the two lines intersect? _________

4. What is the meaning of the point of intersection in the context of this

problem?


_______________________________________________________________

_______________________________________________________________

_______________________________________________________________

5. If it will only take 3 hours to fix your car:

a. Which company would be cheapest? ________________________

b. What is the cost? _______________

Show your work below:

6. If it takes 6 hours to repair the car

a. Which company would be cheapest? __________________________

b. What is the cost? _______________

Show your work below:

7. Which repair shop do you think is advertising to encourage customers with

quick repairs to use their services? Explain why.

_______________________________________________________________

_______________________________________________________________

__________________________________________

Answer 1

MIKE’S REPAIR SHOP: $100 Service Charge plus $65 per hour.

AMY’S AUTO REPAIR: $40 Service Charge plus $80 per hour.

1. Write an equation for each repair shop to represent the total cost of the car

Solution:

Let x = number of hours worked Let y = total cost

MIKE’S REPAIR SHOP  ⇒ y = 100 + 65x

AMY’S AUTO REPAIR  ⇒ y = 40 + 80x

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2. Use the substitution or elimination method to find the point of intersection.

y = 100 + 65x  ⇒ (1)

y = 40 + 80x   ⇒ (2)

Substitute with y from (1) at (2)

100 + 65x = 40 + 80x ⇒ Combine like terms

100 - 40 = 80x - 65x

60 = 15x

x = 60/15 = 4  ⇒ y = 100 + 65*4 = 360

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3. Which auto repair service should I use?

See the attached figure.

As x = number of hours worked Let y = total cost

So, if x < 4 ⇒ you should use AMY’S AUTO REPAIR  ⇒ y = 40 + 80x

So, if x > 4 ⇒ you should use MIKE’S REPAIR SHOP  ⇒ y = 100 + 65x

============================================

4. At what point do the two lines intersect?

As shown in the attached figure the two lines intersects at (4,360)

=============================================

5.  What is the meaning of the point of intersection in the context of this problem?

At the point of intersection which is (4,360)

x = 4 = number of hours worked

y = 360 = total cost

So, the cost is equal at both shops in case of the number of hours worked is 4 hours.

==========================================

6. If it will only take 3 hours to fix your car:

6.1 Which company would be cheapest? ⇒ AMY’S AUTO REPAIR

6.2 What is the cost?  ⇒ cost = 40 + 80*3 = $280

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7.  If it takes 6 hours to repair the car

7.1  Which company would be cheapest? ⇒ MIKE’S REPAIR SHOP

7.2 What is the cost? ⇒ Cost = 100 + 65 * 6 = $490

==================================================

8. Which repair shop do you think is advertising to encourage customers with quick repairs to use their services? Explain why.

For quick repairs x < 4

The cost of repair at AMY’S AUTO is less than the cost of repair at MIKE’S SHOP

So, AMY’S AUTO REPAIR  is advertising to encourage customers with quick repairs to use their services