Let's break down the information provided in this problem to set up the inequality and solve for the minimum hours required.

Problem Breakdown:

1. Monthly Rent: $1,000
2. Monthly Utility Cost: $225
3. Hourly Wage: $8.25 per hour
4. Goal: Determine the minimum hours $x$ needed to work to cover rent and utilities.

Total Monthly Cost:

The combined cost of rent and utilities is: $1000 + 225 = 1225$

Setting Up the Inequality:

To cover this total cost, you need to earn at least $1225 in a month. Let $x$ represent the number of hours worked in a month. The income can be represented by $8.25x$, so the inequality to meet or exceed the expenses is: $8.25x \geq 1225$

Solving for $x$:

To find the minimum hours $x$, divide both sides by 8.25: $x \geq \frac{1225}{8.25}$

Calculating that gives: $x \geq 148.48$

Since you can't work a fraction of an hour in most scenarios, round up to the nearest whole number: $x \geq 149$

Answer:

The minimum number of hours you need to work per month to pay these bills is 149 hours.

Would you like more details or have any other questions?

Related Questions:

1. How would the inequality change if the hourly wage increased?
2. What if there was an additional monthly bill? How would that affect the required hours?
3. How can you calculate the number of hours needed if you have multiple income sources?
4. What if the hourly wage was variable each month? How would that impact the inequality setup?
5. How would working overtime (at a higher rate) affect the number of hours needed?

Tip:

When solving inequalities involving real-world scenarios, always consider rounding up since partial units (like hours) might not always be feasible or practical.