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?

Question

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 \(\boxed{1:16}\).