Question

Bridget measured a city and made a scale drawing. The scale of the drawing was 6 inches = 4 yards. What scale factor does the drawing use?

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

Answer 1

To find the scale factor of the drawing, we need to express the two measurements in the same units. The scale given is 6 inches = 4 yards.

First, we convert yards to inches. Since 1 yard equals 36 inches, we calculate:

\[
4 \text{ yards} = 4 \times 36 \text{ inches} = 144 \text{ inches}
\]

Now, we can express the scale as:

\[
6 \text{ inches} = 144 \text{ inches}
\]

To find the scale factor, we divide both sides by 6:

\[
1 \text{ inch} = \frac{144 \text{ inches}}{6} = 24 \text{ inches}
\]

Thus, the scale factor in terms of inches is:

\[
1 \text{ inch} : 24 \text{ inches}
\]

Now, we can simplify this into a ratio of the lengths, giving us:

\[
1 : 24
\]

Therefore, the scale factor of the drawing is:

\[
\boxed{1:24}
\]