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