Question

Daniel has a choice of where to get his car repaired. Expert autos charges a diagnostic fee of $50 plus $60 per hour in labor. Auto Specialists charge $80 per hour in labor. At how many hours would they both charge the same

Answer 1

Answer: 2.5 hours

Explanation:

let x = hours

80x = 50 + 60x

20x = 50 subtract 60x from both sides

x = 2.5 hours

check

80(2.5) = 50 + 60(2.5)

200 = 50 + 150

200 = 200

Answer 2

2.5 hours

Explanation:

Given information:

• Expert autos charges a diagnostic fee of $50 plus $60 per hour in labor.
• Auto Specialists charge $80 per hour in labor.

Define the variables:

• Let x = the number of hours labor.
• Let y = the total charge (in dollars).

Create two equations with the given information and defined variables to model the total charge per garage.

Expert Autos

`y=60x+50`

Auto Specialists

`y=80x`

To find at how many hours would they both charge the same, substitute the second equation into the first and solve for x:

`\implies 80x=60x+50`

`\implies 20x=50`

`\implies x=2.5`

Therefore, both garages would charge the same at 2.5 hours.