A technician charges a one-time fixed diagnostic fee of \35 plus \25 for each hour of repa… — GRE General Test

A technician charges a one-time fixed diagnostic fee of $\$35$ plus $\$25$ for each hour of repair work. If the total bill for a repair job was $\$160$ , how many hours of repair work were performed?

A
$3$
B
$4$
$5$ Answer
D
$6$
E
$7$

Answer

5 hours

Let

h

represent the number of hours of repair work. The total charge is given by the sum of the fixed fee (

\$35

) and the hourly rate times hours worked (

25h

). Setting up the linear equation

35 + 25h = 160

and isolating

h

gives

25h = 125

, which simplifies to

h = 5

. Thus, 5 hours of work were performed.

Step-by-Step Solution

Define the variable and set up the linear equation

35 + 25h = 160

, where

h

is the number of repair hours.

The total cost is the sum of the fixed diagnostic fee and the hourly charge multiplied by hours worked.

Subtract the fixed fee from both sides of the equation

25h = 160 - 35 \implies 25h = 125

Isolate the variable term containing

h

Divide both sides by the hourly rate coefficient

h = \frac{125}{25} = 5

Solve for

h

Key Concept

Formulating and solving linear equations in one variable from real-world scenarios

Question

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