A proportional relationship with a unit rate of 4 to 1 means that for every 4 units of one quantity, there is 1 unit of another quantity.
Let's evaluate each situation to determine if it matches that unit rate:
A. Actire warehouse has exactly 12,800 automobile tires for 3,200 automobile.
- This implies a ratio of 12,800 tires to 3,200 automobiles.
- Simplifying the ratio: \( \frac{12,800}{3,200} = 4 \).
- This corresponds to a unit rate of 4 tires for every 1 automobile. (MATCHES)
B. Hikers travel 48 miles in 6 hours.
- This gives a ratio of 48 miles to 6 hours.
- Simplifying the ratio: \( \frac{48}{6} = 8 \).
- This corresponds to a unit rate of 8 miles per hour. (DOES NOT MATCH)
C. A DJ is required to play 60 songs over a 4 hour shift.
- This gives a ratio of 60 songs to 4 hours.
- Simplifying the ratio: \( \frac{60}{4} = 15 \).
- This corresponds to a unit rate of 15 songs per hour. (DOES NOT MATCH)
D. A cookie recipe uses 1 3/4 cups of brown sugar for 2 batches.
- Converting 1 3/4 cups to an improper fraction gives \( \frac{7}{4} \) cups for 2 batches.
- The ratio of brown sugar to batches is \( \frac{7/4}{2} \), which simplifies to \( \frac{7}{4} \times \frac{1}{2} = \frac{7}{8} \).
- This is \( \frac{7/8}{1} \) for every batch, which is not 4 to 1. (DOES NOT MATCH)
The situation that represents a proportional relationship with a unit rate of 4 to 1 is:
A. Actire warehouse has exactly 12,800 automobile tires for 3,200 automobile.