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We are asked to solve the following problem using proportions:

**Problem:**
- A 30-pound bag of topsoil covers a surface area of 12 ft².
- The task is to determine how many pounds of topsoil are needed to cover a surface area of 480 ft², and how many bags of topsoil must be purchased.

### Part a) Pounds of topsoil needed to cover 480 ft²:
We can set up a proportion based on the given information.

\[
\frac{30 \, \text{pounds}}{12 \, \text{ft}^2} = \frac{x \, \text{pounds}}{480 \, \text{ft}^2}
\]

Now, we solve for $ x $ (the number of pounds needed):

\[
x = \frac{30 \times 480}{12} = \frac{14400}{12} = 1200 \, \text{pounds}
\]

So, **1200 pounds** of topsoil are needed to cover 480 ft².

### Part b) Number of bags of topsoil required:
Each bag weighs 30 pounds, so to determine how many bags are needed for 1200 pounds:

\[
\text{Number of bags} = \frac{1200 \, \text{pounds}}{30 \, \text{pounds per bag}} = 40 \, \text{bags}
\]

Thus, **40 bags** of topsoil must be purchased to cover 480 ft².

---

Would you like more details or clarifications? Here are five related questions for further practice:

1. How much topsoil (in pounds) would be needed to cover 600 ft²?
2. If a bag of topsoil could cover 15 ft² instead, how many pounds would be required for 480 ft²?
3. What if a 25-pound bag covers 12 ft², how many pounds would you need for 480 ft²?
4. How many pounds of topsoil are needed for a surface area of 360 ft²?
5. If the price per bag is $5, how much would it cost to cover 480 ft²?

**Tip:** When working with proportions, remember to keep your units consistent throughout the problem!

A 30-pound bag of topsoil will cover a surface area of 12 ft². How many pounds of topsoil are needed to cover a surface area of 480 ft²? How many bags of topsoil must be purchased to cover a surface area of 480 ft²?

Learn how to calculate the amount of topsoil needed to cover 480 ft² using proportions. This step-by-step solution demonstrates how to apply ratios and proportions to real-life problems involving surface area and weight. Suitable for students in Grades 6-8.

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