Question
8. Bob has a scale drawing of his kitchen with a scale of \( 4 \mathrm{in} .=5 \mathrm{ft} \). If his kitchen is 12.5 feet in width, what is the width on the scale drawing (inches)?
Ask by Higgins Burns. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The width on the scale drawing is 10 inches.
Solution
To determine the width of Bob's kitchen on the scale drawing, follow these steps:
1. **Understand the Scale:**
The scale provided is \( 4 \) inches on the drawing equals \( 5 \) feet in real life. This can be written as:
\[
\frac{4 \text{ inches}}{5 \text{ feet}} = \frac{x \text{ inches}}{12.5 \text{ feet}}
\]
2. **Set Up the Proportion:**
\[
\frac{4}{5} = \frac{x}{12.5}
\]
3. **Solve for \( x \):**
Multiply both sides of the equation by \( 12.5 \) to isolate \( x \):
\[
x = \frac{4}{5} \times 12.5
\]
\[
x = 10 \text{ inches}
\]
4. **Conclusion:**
The width of Bob's kitchen on the scale drawing is **10 inches**.
**Answer:**
The width on the scale drawing is 10 inches.
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Simplify this solution Beyond the Answer
To find the width on the scale drawing, we start by converting Bob's kitchen width from feet to inches using the scale provided. Given that \( 4 \text{ in} = 5 \text{ ft} \), we can set up a proportion to find the corresponding width in inches: 1. First, determine how many inches correspond to 1 foot by dividing 4 inches by 5 feet: \[ \frac{4 \text{ in}}{5 \text{ ft}} = \frac{x \text{ in}}{12.5 \text{ ft}} \] 2. To isolate \( x \), we can cross-multiply and get: \[ x \text{ in} = 12.5 \text{ ft} \times \frac{4 \text{ in}}{5 \text{ ft}} = 12.5 \times \frac{4}{5} \] \[ = 12.5 \times 0.8 = 10 \text{ in} \] Thus, the width on the scale drawing is **10 inches**.
