Juanita has $25 and she makes $11 per hour. She needs at least $58 to buy new shoes. How many hours must Juanita work?

What the problem is asking

Juanita already has some money saved and earns a fixed amount per hour. We need to find the minimum number of hours so her total money is at least $58$.

Write an inequality for her total money

• Money she starts with: $25$
• Money she earns after $h$ hours: $11h$

Total money after $h$ hours is $25 + 11h$. She needs at least $58$, so: $$25 + 11h \ge 58$$

Solve for $h$

Subtract 25 from both sides: $$11h \ge 58 - 25 = 33$$ Divide both sides by 11: $$h \ge \frac{33}{11} = 3$$

Check the result

After 3 hours she earns $11 \cdot 3 = 33$ dollars, and $25 + 33 = 58$, which meets the “at least $58$” requirement.