system of linear equations

Question

Two mechanics worked on a car. The first mechanic worked for
10 hours, and the second mechanic worked for 15
hours.

Together they charged a total of $2475.

What was the rate charged per hour by each mechanic if the sum of the two rates was
$200 per hour?

Answer 1

Hi Cierra.

 

For systems of linear equations it's always best to call some variables at the beginning. Be sure to define them very well so that at the end of the problem, when you look back at your value, you know exactly what it represents. In this question, you're asked to find the rates of pay.

 

I'm going to say that:

 

T = rate of pay for the mechanic who worked 10 hours.

F = rate of pay for the mechanic who worked 15 hours.

 

It says the sum of their rates is $200 per hour. That means:

 

T + F = 200

 

We also know that together they earned $2475. That means:

 

10*T + 15*F = 2475

 

This equation is stating "10 hours times that mechanic's rate of pay, plus 15 hours times that mechanic's rate of pay is equal to the total dollar amount they each brought in."

 

So now you have two equations, two unknowns.

 

T + F = 200

10T + 15F = 2475

 

Multiply the top equation by -10 and add the two equations together to eliminate the T.

 

-10T - 10F = -2000

10T + 15F = 2475

 

5F = 475

 

F = 95

 

This means that the mechanic who worked 15 hours makes $95/ hour

 

Since

 

T + F = 200

 

T + 95 = 200

 

T = 105

 

This means the mechanic who worked 10 hours makes $105/ hour

 

Always good to check your results:

 

10T + 15F = 2475

 

10*105 + 15*95 = 2475

 

1050 + 1475 = 2475

 

2475 = 2475

 

Looks good.

 

Hope this helps.