Question

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the dimensions of sara’s apartment are $22\frac{1}{2}$ feet by 25 feet. in the drawing of the apartment below, $\frac{1}{2}$ inches is equivalent to 15 feet.
complete the sentence below.
the unit rate of the areas is square feet of the apartment per square inch of the drawing.

Explanation:

Step1: Find the area of the apartment in square feet

The actual dimensions of the apartment are \( 22\frac{1}{2} \) feet (which is \( \frac{45}{2} \) feet) and \( 25 \) feet. The area \( A_{actual} \) is length times width, so \( A_{actual}=\frac{45}{2}\times25=\frac{1125}{2} = 562.5 \) square feet.

Step2: Find the area of the drawing in square inches

The dimensions of the drawing are \( 2\frac{1}{2} \) inches (which is \( \frac{5}{2} \) inches) and \( 2\frac{1}{4} \) inches (which is \( \frac{9}{4} \) inches). The area \( A_{drawing} \) is length times width, so \( A_{drawing}=\frac{5}{2}\times\frac{9}{4}=\frac{45}{8} = 5.625 \) square inches.

Step3: Calculate the unit rate

The unit rate is the actual area divided by the drawing area, so \( \text{Unit Rate}=\frac{562.5}{5.625}=100 \).

Answer:

100