Extremely mathy math and is very math

Question

Sophie needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4 hours and charged her $127 for parts. The total was $227. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.

Answer 1

So x is the variable that represents the charge in $ per hour that is charged by the tech. Since he worked for 4 hours his total charge for labor was $4x. In addition he charged $127 for parts.

So the total charge can be represented by: 4x + 127. For example if he charged $2 per hour, then the charge would have been 4(2) + 127 = 135.

But we are told that the total charge was in fact $227. So the equation that models the problem:

4x + 127 = 227. Solving that equation for x will determine what the tech actually charged for each hour of work.

4x = 100 (subtraction property for equality, subtracting 127 from each side).

x = 100/4 (division property for equality, dividing both sides by the coefficient of x which is 4).

x = 25

Check:

For 4 hours of work at $25 for each hour, the labor charge is 4(25) = 100.

Add on the $127 for parts; total charge is $100 + $127 = $227.

Answer 2

if you let "x" represent the cost per labor hour then the equation here ends up being

4x + 127 = 227

then solving that algebraically for the value of x yields

4x + 127 = 227

4x = 100

x = 25

meaning that the cost of the labor per hour is $25/hour