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:

\[ h \geq 25 \]