To find the unit rate of the areas, we'll first calculate the area of Sara's apartment in square feet and the area represented in the drawing in square inches.
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Calculate the area of the apartment:
- The dimensions of the apartment are 22 1/2 feet by 25 feet.
- Convert 22 1/2 feet to an improper fraction: 22.5 feet = 22.5 feet × 1 = 22.5 feet.
- Area = length × width = 22.5 feet × 25 feet = 562.5 square feet.
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Calculate the area represented in the drawing:
- We need to determine the dimensions of the apartment in the drawing. Given that 1 1/2 inches is equivalent to 15 feet, we first set up the ratio:
- 1.5 inches corresponds to 15 feet.
- We convert the dimensions of the apartment from feet to inches based on this scale.
- For 22.5 feet: \(\frac{22.5}{15} \times 1.5\) inches = 2.25 inches (approximately).
- For 25 feet: \(\frac{25}{15} \times 1.5\) inches = 2.5 inches (approximately).
- We need to determine the dimensions of the apartment in the drawing. Given that 1 1/2 inches is equivalent to 15 feet, we first set up the ratio:
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Calculate the area of the drawing:
- Area of the drawing = drawing length × drawing width = 2.25 inches × 2.5 inches = 5.625 square inches.
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Calculate the unit rate of the areas:
- To find the unit rate, divide the area of the apartment by the area of the drawing.
- Unit rate = area of apartment / area of drawing = 562.5 square feet / 5.625 square inches.
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Calculating the unit rate:
- \[ = \frac{562.5 \text{ square feet}}{5.625 \text{ square inches}} \approx 100 \text{ square feet per square inch.} \]
Therefore, the unit rate of the areas is 100 square feet of the apartment per square inch of the drawing.
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