Question

Josh drew a scale drawing of a game room. In real life, the pool table is 4 feet wide. It is 3 inches wide in the drawing. What is the drawing's scale factor?

Simplify your answer and write it as a ratio, using a colon.

Answer 1

To find the scale factor of the drawing, we first need to convert the dimensions to the same units.

1. The real-life width of the pool table is 4 feet. Since there are 12 inches in a foot, we can convert feet to inches:
\[
4 \text{ feet} = 4 \times 12 = 48 \text{ inches}
\]

2. The width of the pool table in the drawing is 3 inches.

Now we can set up the scale factor as a ratio of the drawing size to the real size:
\[
\text{Scale factor} = \frac{\text{Drawing size}}{\text{Real size}} = \frac{3 \text{ inches}}{48 \text{ inches}}
\]

3. We can simplify this fraction:
\[
\frac{3}{48} = \frac{1}{16}
\]

4. Therefore, the scale factor is:
\[
1:16
\]

Thus, the drawing's scale factor is \(\boxed{1:16}\).