Question

Hanna earns a base salary of $75 per week plus $9 for each hour she works. The inequality can be used to determine h, the minimum number of hours she must work to earn $300 during one week.

Answer 1

To determine the minimum number of hours \( h \) that Hanna must work to earn at least $300 in one week, we can set up the following inequality.

Hanna's total earnings for the week can be expressed as:

\[
\text{Total earnings} = \text{Base salary} + \text{Hourly wage} \times \text{Number of hours worked}
\]

Substituting in her base salary of $75 and her hourly wage of $9, we have:

\[
\text{Total earnings} = 75 + 9h
\]

We want this total to be at least $300, so we set up the inequality:

\[
75 + 9h \geq 300
\]

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

1. Subtract 75 from both sides:

\[
9h \geq 300 - 75
\]
\[
9h \geq 225
\]

2. Divide both sides by 9:

\[
h \geq \frac{225}{9}
\]
\[
h \geq 25
\]

Thus, the inequality that can be used to determine \( h \), the minimum number of hours she must work to earn at least $300 during one week, is:

\[
h \geq 25
\]