A computer technician charges a flat fee of $35 to repair a computer in addition to an hourly rate of $22.50. The technician has calculated he will earn at least $215 from his next repair job. Which inequality can be used to determine the number of hours, h, that the technician will work on his next job?

Question

A.
, with a solution of

B.
, with a solution of

C.
, with a solution of

D.
, with a solution of

Answer 1

To model the earnings of the computer technician, we can break it down into the following components:

1. Flat fee: $35
2. Hourly rate: $22.50 per hour
3. Total earnings must be at least $215

We can represent the total earnings \( E \) as follows:

\[ E = 35 + 22.50h \]

To find the inequality that describes when the technician earns at least $215, we set up the inequality:

\[ 35 + 22.50h \geq 215 \]

Now, we can solve for \( h \):

1. Subtract 35 from both sides:

\[ 22.50h \geq 215 - 35 \] \[ 22.50h \geq 180 \]

2. Divide both sides by 22.50:

\[ h \geq \frac{180}{22.50} \] \[ h \geq 8 \]

So the inequality we derived is:

\[ 35 + 22.50h \geq 215 \]

And the solution indicates that the technician must work at least 8 hours.

Considering the possible answer choices (A, B, C, D), the correct option is D. because it matches our identified inequality and its solution. To ensure you match it with the options, look for the inequality \( 35 + 22.50h \geq 215 \) and the solution \( h \geq 8 \).