Question

Eva measured the auditorium and made a scale drawing. He used the scale 23 inches and 6 feet if the actual width of the stage is 16 feet how wide is the stage in the drawing?

Answer 1

To find out how wide the stage is in the drawing, we can first determine the scale of the drawing used by Eva. The scale given is 23 inches for 6 feet.

1. Convert the actual width of the stage to inches, because the scale is given in inches. Since 1 foot is 12 inches, we can convert 6 feet to inches:

\[
6 \text{ feet} = 6 \times 12 = 72 \text{ inches}
\]

2. Now, we have the scale as follows: 23 inches on the drawing represents 72 inches in reality.

3. We need to find the width of the stage in the drawing when the actual width is 16 feet:

Convert 16 feet to inches:

\[
16 \text{ feet} = 16 \times 12 = 192 \text{ inches}
\]

4. Now we set up a proportion based on the scale:

\[
\frac{23 \text{ inches}}{72 \text{ inches}} = \frac{x \text{ inches}}{192 \text{ inches}}
\]

Where \(x\) is the width in the drawing.

5. Cross-multiply to solve for \(x\):

\[
23 \times 192 = 72 \times x
\]

Calculating \(23 \times 192\):

\[
23 \times 192 = 4416
\]

6. Thus, the equation becomes:

\[
4416 = 72x
\]

7. Now, divide both sides by 72 to find \(x\):

\[
x = \frac{4416}{72} = 61.3333
\]

This can be converted into a fraction:

\[
\frac{4416}{72} = 61 \frac{1}{3} \text{ inches}
\]

8. Therefore, the width of the stage in the drawing is approximately **61.33 inches** or **61 and 1/3 inches.**