Question
Johnny drew a scale drawing of an apartment. The scale he used was 8 inches : 3 feet. In the drawing, the broom closet is 16 inches long. What is the length of the actual closet?
feet
feet
Answers
GPT-4o mini
To find the actual length of the broom closet, we can use the scale provided: 8 inches in the drawing corresponds to 3 feet in reality.
First, we'll set up a proportion based on the scale.
The scale tells us:
\[
8 \text{ inches} : 3 \text{ feet}
\]
We know the length of the broom closet in the drawing is 16 inches. Let \( x \) be the actual length of the closet in feet. We can set up the proportion:
\[
\frac{8 \text{ inches}}{3 \text{ feet}} = \frac{16 \text{ inches}}{x \text{ feet}}
\]
Now, we can cross-multiply to solve for \( x \):
\[
8x = 16 \cdot 3
\]
Calculating the right side:
\[
8x = 48
\]
Next, divide both sides by 8 to solve for \( x \):
\[
x = \frac{48}{8} = 6
\]
Thus, the actual length of the broom closet is \( \boxed{6} \) feet.
First, we'll set up a proportion based on the scale.
The scale tells us:
\[
8 \text{ inches} : 3 \text{ feet}
\]
We know the length of the broom closet in the drawing is 16 inches. Let \( x \) be the actual length of the closet in feet. We can set up the proportion:
\[
\frac{8 \text{ inches}}{3 \text{ feet}} = \frac{16 \text{ inches}}{x \text{ feet}}
\]
Now, we can cross-multiply to solve for \( x \):
\[
8x = 16 \cdot 3
\]
Calculating the right side:
\[
8x = 48
\]
Next, divide both sides by 8 to solve for \( x \):
\[
x = \frac{48}{8} = 6
\]
Thus, the actual length of the broom closet is \( \boxed{6} \) feet.