To find the situation that represents the proportional relationship with a unit rate of 4 to 1, we need to identify which option has a ratio that simplifies to 4:1.
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A tire warehouse has exactly 12,800 automobile tires for 3,200 automobiles.
- Ratio: \( \frac{12,800}{3,200} = 4 \)
- This shows a unit rate of 4 tires per automobile.
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Hikers travel 48 miles in 6 hours.
- Ratio: \( \frac{48}{6} = 8 \)
- This does not match a unit rate of 4 to 1.
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A DJ is required to play 60 songs over a 4-hour shift.
- Ratio: \( \frac{60}{4} = 15 \)
- Again, this does not match a unit rate of 4 to 1.
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A cookie recipe uses 1 3/4 cups of brown sugar for 2 batches.
- First, convert 1 3/4 to an improper fraction: \( 1 \frac{3}{4} = \frac{7}{4} \).
- Ratio: \( \frac{\frac{7}{4}}{2} = \frac{7}{4} \times \frac{1}{2} = \frac{7}{8} \)
- This does not match a unit rate of 4 to 1.
The only situation that represents a proportional relationship with a unit rate of 4 to 1 is:
A tire warehouse has exactly 12,800 automobile tires for 3,200 automobiles.
2 answers