Question

a blueprint of a new home has a scale of 3 inches : 8 feet. a wall in the bonus room has a length of $7\frac{1}{2}$ inches on the blueprint. how long is the actual bonus room wall?\
a $12\frac{1}{2}$ feet\
b $18\frac{2}{3}$ feet\
c 20 feet\
d 24 feet

Explanation:

Step1: Define the scale ratio

The scale is 3 inches : 8 feet, which means $\frac{3 \text{ inches}}{8 \text{ feet}}$. Let the actual length be $x$ feet. The blueprint length is $7\frac{1}{2}=\frac{15}{2}$ inches.

Step2: Set up the proportion

We set up the proportion $\frac{3}{8}=\frac{\frac{15}{2}}{x}$. Cross - multiply to get $3x = 8\times\frac{15}{2}$.

Step3: Solve for x

First, calculate $8\times\frac{15}{2}=4\times15 = 60$. Then, $3x=60$, so $x=\frac{60}{3}=20$. Wait, no, wait. Wait, the scale is 3 inches represents 8 feet. So the ratio of blueprint inches to actual feet is 3:8. So if the blueprint length is $7.5$ inches, let the actual length be $x$ feet. Then $\frac{3}{8}=\frac{7.5}{x}$. Cross - multiply: $3x=8\times7.5$. $8\times7.5 = 60$. Then $x=\frac{60}{3}=20$? Wait, but let's check again. Wait, $7\frac{1}{2}$ inches is $7.5$ inches. The scale is 3 inches for 8 feet. So how many times does 3 go into 7.5? $7.5\div3 = 2.5$. Then the actual length is $2.5\times8=20$ feet. So the answer is C. 20 feet.

Answer:

C. 20 feet