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To solve this problem, we need to calculate the cost per square foot for the brick patio and then use that to estimate the cost of a larger patio.

### Given information:
- The cost of a **15 ft by 20 ft** brick patio is **$2,275**.
- The dimensions of the new patio are **24 ft by 30 ft**.

#### Step 1: Calculate the area of both patios
- **Area of the original patio**:  
  $ 15 \, \text{ft} \times 20 \, \text{ft} = 300 \, \text{square feet} $
  
- **Area of the new patio**:  
  $ 24 \, \text{ft} \times 30 \, \text{ft} = 720 \, \text{square feet} $

#### Step 2: Calculate the cost per square foot
To find the cost per square foot of the original patio:
\[
\text{Cost per square foot} = \frac{2275}{300} = 7.58 \, \text{dollars per square foot}
\]

#### Step 3: Estimate the cost for the new patio
Now, multiply the area of the new patio by the cost per square foot:
\[
\text{Cost of new patio} = 720 \, \text{square feet} \times 7.58 \, \text{dollars per square foot} = 5457.60
\]

Rounding to the nearest dollar, the estimated cost is **$5,458**.

Would you like more details or have any questions about this calculation?

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Here are five related questions to expand on this concept:
1. How would the cost change if the new patio was 10% larger in size?
2. What would be the cost if the price per square foot increased by 10%?
3. How can we estimate the cost if labor rates increase over time?
4. If the materials cost $6 per square foot, what would be the total cost for the patio?
5. How does the area of a patio affect the total installation cost in terms of scaling?

**Tip:** When dealing with cost estimates, calculating the price per unit (like square foot) is essential for scaling costs efficiently!

Estimate the cost of having a 24 ft by 30 ft brick patio installed based on the fact that a 15 ft by 20 ft brick patio would cost $2,275 to have professionally installed. Round your answer to the nearest dollar.

Learn how to estimate the cost of installing a 24 ft by 30 ft brick patio based on the known cost of a smaller patio. This problem involves area calculation, cost per square foot, and proportional scaling. Suitable for students in Grades 7-10.

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