Question

Jeffrey made a scale drawing of a house and its lot. He used the scale 7 inches : 4 feet. If the actual width of the backyard is 48 feet, how wide is the yard in the drawing?

Answer 1

To find the width of the backyard in Jeffrey's drawing, we can use the scale he provided, which is 7 inches in the drawing corresponds to 4 feet in reality.

First, we need to set up a proportion based on the scale:

\[
\frac{7 \text{ inches}}{4 \text{ feet}} = \frac{x \text{ inches}}{48 \text{ feet}}
\]

where \(x\) is the width of the yard in the drawing.

Cross-multiply to solve for \(x\):

\[
7 \text{ inches} \times 48 \text{ feet} = 4 \text{ feet} \times x \text{ inches}
\]

Calculating the left side:

\[
7 \times 48 = 336
\]

So we have:

\[
336 = 4x
\]

Now, divide both sides by 4 to solve for \(x\):

\[
x = \frac{336}{4} = 84
\]

Thus, the width of the backyard in the drawing is:

\[
\boxed{84} \text{ inches}
\]