To find the unit rate of the areas of Sara's apartment per square inch of the drawing, we will first calculate the area of the apartment in square feet and then convert this area into square inches in the drawing.
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Calculate the Area of the Apartment: The dimensions of the apartment are 22.5 feet by 25 feet.
\[ \text{Area} = \text{length} \times \text{width} = 22.5 , \text{feet} \times 25 , \text{feet} = 562.5 , \text{square feet} \]
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Determine the Scale of the Drawing: The scale provided is 1.5 inches is equivalent to 15 feet.
To find out how many square feet correspond to one square inch in the drawing, we need to convert the dimensions in feet to dimensions in inches using the scale.
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Since 1.5 inches represents 15 feet, we can determine how many feet correspond to 1 inch as follows: \[ 15 , \text{feet} \div 1.5 , \text{inches} = 10 , \text{feet per inch} \]
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Therefore, 1 inch on the drawing corresponds to 10 feet in reality.
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Calculating Area per Inch in the Drawing: Since we know the real-world equivalent, we can find the area represented by 1 square inch:
- The area covered by 1 inch by 1 inch in the drawing corresponds to: \[ \text{Area} = 10 , \text{feet} \times 10 , \text{feet} = 100 , \text{square feet} \]
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Calculate the Unit Rate: Now we calculate how many square feet of the apartment correspond to 1 square inch of the drawing:
- Since 1 square inch represents 100 square feet, the conversion from square feet of the apartment to square inches of the drawing is given by: \[ \text{Unit Rate} = \frac{\text{Area of the Apartment}}{\text{Area per Square Inch of Drawing}} = \frac{562.5 , \text{square feet}}{1 , \text{square inch}} \]
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Calculating the Unit Rate: Using the area per square inch determined earlier: \[ \text{Unit Rate} = \frac{562.5 , \text{square feet}}{100 , \text{square feet}} = 5.625 , \text{square feet per square inch} \]
Thus, the complete sentence would be:
"The unit rate of the areas is 5.625 square feet of the apartment per square inch of the drawing."
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