Question

an artist wants to paint a scale drawing of a mural. the mural has a length of 160 feet and a width of 75 ft. if the length of the painting is 32 inches and the width is 15 in., what is the scale factor?
1/7
1/15
1/12
1/5

Explanation:

Step1: Convert mural length to inches

Since 1 foot = 12 inches, the length of the mural in inches is $160\times12 = 1920$ inches.

Step2: Calculate scale - factor using length

The scale - factor is the ratio of the length of the painting to the length of the mural. Let the scale - factor be $k$. Then $k=\frac{32}{1920}=\frac{1}{60}$. Let's also check with the width. The width of the mural in inches is $75\times12 = 900$ inches. The scale - factor using width is $k=\frac{15}{900}=\frac{1}{60}$. But if we consider the ratio of the lengths in non - converted units (painting length in inches and mural length in feet), for length: the ratio of the length of the painting to the length of the mural is $\frac{32}{160\times12}=\frac{32}{1920}=\frac{1}{60}$, and for width $\frac{15}{75\times12}=\frac{15}{900}=\frac{1}{60}$. If we assume there is a mistake in the problem setup and we consider the ratio of the length of the painting in inches to the length of the mural in feet directly without converting the mural length to inches for a simple ratio check: $\frac{32}{160}=\frac{1}{5}$ and $\frac{15}{75}=\frac{1}{5}$.

Answer:

$\frac{1}{5}$