Question
Steven made a scale drawing of a theater. The stage is 5 inches wide in the drawing. The actual stage is 20 feet wide. What is the scale of the drawing?
Answers
GPT-4o mini
To find the scale of the drawing, we need to compare the width of the stage in the drawing to its actual width.
1. **Convert the actual width from feet to inches**:
Since there are 12 inches in a foot, we can convert 20 feet to inches:
\[
20 \text{ feet} \times 12 \text{ inches/foot} = 240 \text{ inches}
\]
2. **Set up the ratio for the scale**:
The scale can be expressed as a ratio of the width in the drawing to the actual width:
\[
\text{Scale} = \frac{\text{Width in drawing}}{\text{Actual width}} = \frac{5 \text{ inches}}{240 \text{ inches}}
\]
3. **Simplify the ratio**:
We can simplify \(\frac{5}{240}\) by dividing both the numerator and denominator by 5:
\[
\frac{5 \div 5}{240 \div 5} = \frac{1}{48}
\]
Therefore, the scale of the drawing is:
\[
\text{Scale} = 1 : 48
\]
This means that 1 inch on the drawing represents 48 inches (or 4 feet) in reality.
1. **Convert the actual width from feet to inches**:
Since there are 12 inches in a foot, we can convert 20 feet to inches:
\[
20 \text{ feet} \times 12 \text{ inches/foot} = 240 \text{ inches}
\]
2. **Set up the ratio for the scale**:
The scale can be expressed as a ratio of the width in the drawing to the actual width:
\[
\text{Scale} = \frac{\text{Width in drawing}}{\text{Actual width}} = \frac{5 \text{ inches}}{240 \text{ inches}}
\]
3. **Simplify the ratio**:
We can simplify \(\frac{5}{240}\) by dividing both the numerator and denominator by 5:
\[
\frac{5 \div 5}{240 \div 5} = \frac{1}{48}
\]
Therefore, the scale of the drawing is:
\[
\text{Scale} = 1 : 48
\]
This means that 1 inch on the drawing represents 48 inches (or 4 feet) in reality.