Question

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?

A.
,22.5h+35>215 with a solution of h>8

B.
,35h+22.5>215 with a solution of h >5.5

C.
, with a solution of

D.
, with a solution of

Answer 1

To determine the correct inequality for the computer technician's charges, we can break down the total earnings from a repair job.

The technician charges a flat fee of $35 for the service, plus an hourly rate of $22.50 for each hour worked. Therefore, the total amount earned \( E \) can be represented as:

\[
E = 35 + 22.5h
\]

where \( h \) is the number of hours worked.

The technician wants to earn at least $215, so we can set up the inequality as follows:

\[
35 + 22.5h \geq 215
\]

To solve for \( h \):

1. Subtract 35 from both sides:

\[
22.5h \geq 215 - 35
\]

\[
22.5h \geq 180
\]

2. Now, divide both sides by 22.5:

\[
h \geq \frac{180}{22.5}
\]

Calculating \( \frac{180}{22.5} \) gives:

\[
h \geq 8
\]

Thus, the inequality that represents the condition is:

\[
22.5h + 35 \geq 215
\]

So the correct choice is:

**A. \( 22.5h + 35 > 215 \) with a solution of \( h > 8 \)**