Algebra Mechanic System of Equations Question

Question

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of 1600. What was the rate charged per hour by each mechanic if the sum of the two rates was 215 per hour?

Answer 1

Write an equation to calculate the cost of the repair = $1600 =RateA*10+RateB*5. Note that the sum of the rates is given at $215/hour=RateA+RateB. Solve these equations by substitution noting first that RateA=215-RateB and substituting that expression into the cost equation making 1600=(215-RateB)*10+RateB*5. Solve that for RateB=$105/hour. Use RateA+RateB=215 and substitute 105 for RateB finding RateA= $110/hour.

Answer 2

Lets make the rate of the first mechanic be x.

Lets make the rate of the second mechanic be y.

Given that the sum of the two rates of x and y is $215 per hour we can set up two equations.

x + y = 215

y = 215 - x

The cost of the first mechanic is 10x and the cost of the second mechanic is 5y and it's given that the total cost for both is $1600. So we can set up another equation with this given information.

10x + 5y = 1600

Now plug in our value for y into the equation we just made.

10x + 5(215-x) = 1600

10x + 1075 - 5x = 1600

5x + 1075 = 1600

5x = 525

x = 105

Now plug in what we got as x into the equation that we made with y = 215 - x.

y = 215 - 105

y = 110

The first mechanic's rate charged per hour is $105/hr and the second mechanic's rate charged per hour is $110/hr.