You read online that a 15 ft by 20 ft brick patio would cost about $2,275 to have professionally installed. Estimate the cost of having a 19 by 30 ft brick patio installed. Round your answer to the nearest dollar.

The cost of installing a 15 ft by 20 ft patio is $2,275. To estimate the cost of a 19 ft by 30 ft patio, we can compare the areas of the two patios and assume the cost is proportional to the area.

### Step 1: Calculate the area of both patios
- **Area of the 15 ft by 20 ft patio**:
  \[
  15 \times 20 = 300 \, \text{square feet}
  \]
  
- **Area of the 19 ft by 30 ft patio**:
  \[
  19 \times 30 = 570 \, \text{square feet}
  \]

### Step 2: Find the cost per square foot
The cost for the 300 square foot patio is $2,275. Therefore, the cost per square foot is:
\[
\frac{2275}{300} \approx 7.58 \, \text{dollars per square foot}
\]

### Step 3: Estimate the cost for the 19 by 30 ft patio
Now, we can estimate the cost for the 570 square foot patio by multiplying the cost per square foot by the new area:
\[
570 \times 7.58 \approx 4,320.60
\]
Rounding to the nearest dollar, the estimated cost is **$4,321**.

Would you like any additional details or have any questions?

Here are some related questions:
1. How would the cost change if the price per square foot increased by 10%?
2. How do you calculate the area of irregularly shaped patios?
3. What factors might affect the cost per square foot for different installations?
4. How could labor costs impact the total installation cost?
5. Can this method be applied to other materials like concrete or pavers?

**Tip**: Always check if labor costs and material costs are included in the estimate per square foot!

Estimate the cost of installing a 19 ft by 30 ft brick patio using proportionality based on a 15 ft by 20 ft patio priced at $2,275. This guide walks through calculating area, cost per square foot, and estimating the total installation cost, perfect for middle school math students.

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