Question

Set up a proportion then solve to get your scale dimensions. Yards / inches = 8 yards / 1 inch. Actual dimensions: length = 60 yards; width = 40 yards

Answer 1

To set up a proportion based on the scale provided, we can relate the actual dimensions of the yard to the scale dimensions given in the problem.

The proportion given is:
\[
\frac{\text{yards}}{\text{inches}} = \frac{8 \text{ yards}}{1 \text{ inch}}
\]

We need to convert the actual dimensions of the area (length = 60 yards, width = 40 yards) into the scale dimensions using the proportion.

### Step 1: Set Up the Proportion

1. For Length:
\[
\frac{60 \text{ yards}}{x \text{ inches}} = \frac{8 \text{ yards}}{1 \text{ inch}}
\]

2. For Width:
\[
\frac{40 \text{ yards}}{y \text{ inches}} = \frac{8 \text{ yards}}{1 \text{ inch}}
\]

### Step 2: Solve for x (Scale Length)

Cross-multiply for the length proportion:
\[
60 \text{ yards} \cdot 1 \text{ inch} = 8 \text{ yards} \cdot x \text{ inches}
\]

This simplifies to:
\[
60 = 8x
\]

Now, solve for \(x\):
\[
x = \frac{60}{8} = 7.5 \text{ inches}
\]

### Step 3: Solve for y (Scale Width)

Cross-multiply for the width proportion:
\[
40 \text{ yards} \cdot 1 \text{ inch} = 8 \text{ yards} \cdot y \text{ inches}
\]

This simplifies to:
\[
40 = 8y
\]

Now, solve for \(y\):
\[
y = \frac{40}{8} = 5 \text{ inches}
\]

### Conclusion

The scale dimensions based on the proportion and actual dimensions are:
- **Scale Length** = 7.5 inches
- **Scale Width** = 5 inches