Question

Jackson earns $25 as a tutor at the library. He set a weekly spending budget of $130 each week and puts the remaining money in his savings account. How many hours must he work this week in order to have at least an extra $50 to put in his savings account?

Write and solve an inequality to represent this situation. Show all steps. You must show ALL work to earn full credit.

Answer 1

To determine how many hours Jackson must work this week in order to have at least an extra $50 to put in his savings account after covering his spending budget, we can set up the problem as follows:

1. **Define Variables**:
Let \( h \) be the number of hours Jackson works.

2. **Determine Earnings**:
Jackson earns $25 per hour as a tutor. Therefore, his total earnings for \( h \) hours will be:
\[
\text{Earnings} = 25h
\]

3. **Set Up the Budget**:
Jackson has a weekly spending budget of $130. We need to determine how much he can save after covering this budget:
\[
\text{Money left after spending} = \text{Earnings} - \text{Budget} = 25h - 130
\]

4. **Establish Savings Goal**:
Jackson wants to have at least an extra $50 for savings. Therefore, we can set up the inequality:
\[
25h - 130 \geq 50
\]

5. **Solve the Inequality**:
Now we will solve the inequality step-by-step.
\[
25h - 130 \geq 50
\]
First, add 130 to both sides:
\[
25h \geq 50 + 130
\]
\[
25h \geq 180
\]
Next, divide both sides by 25:
\[
h \geq \frac{180}{25}
\]
Simplifying the fraction:
\[
h \geq 7.2
\]

6. **Interpret the Result**:
Since Jackson cannot work a fraction of an hour, he must round up to the nearest whole number. Therefore, he must work at least:
\[
h = 8 \text{ hours}
\]

**Conclusion**:
Jackson must work **at least 8 hours** this week in order to have at least an extra $50 to put in his savings account.