A proportional relationship has a unit rate of 4 to 1. Which situation below represents this relationship?
A tire warehouse has exactly 12,800 automobile tires for 3,200 automobiles
Hikers travel 48 miles in 6 hours
A DJ is required to play 60 songs over a 4-hour shift
A cookie recipe uses 1 3/4 cups of brown sugar for 2 batches
The situation that represents a proportional relationship with a unit rate of 4 to 1 is the cookie recipe that uses 1 3/4 cups of brown sugar for 2 batches.
The 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.
To find the situation that represents a proportional relationship with a unit rate of 4 to 1, we need to identify the scenario where the values are in a ratio of 4:1.
Let's analyze each situation:
Situation 1: A tire warehouse has exactly 12,800 automobile tires for 3,200 automobiles.
In this case, the ratio of tires to automobiles is 12,800:3,200, which simplifies to 4:1. Therefore, this situation has a proportional relationship with a unit rate of 4 to 1.
Situation 2: Hikers travel 48 miles in 6 hours.
Here, the ratio of miles to hours is 48:6, which simplifies to 8:1. The unit rate is not 4 to 1, so this situation does not represent a proportional relationship with a unit rate of 4 to 1.
Situation 3: A DJ is required to play 60 songs over a 4-hour shift.
The ratio of songs to hours is 60:4, which simplifies to 15:1. Therefore, this situation does not have a proportional relationship with a unit rate of 4 to 1.
Situation 4: A cookie recipe uses 1 3/4 cups of brown sugar for 2 batches.
Here, the ratio of cups of brown sugar to batches is 1 3/4: 2. To compare these fractions, we need to find a common denominator: in this case, 4. Multiplying the numerator and denominator of 1 3/4 by 4, we get 7/4. So, the ratio becomes 7/4:2, which does not simplify to 4:1. Hence, this situation does not represent a proportional relationship with a unit rate of 4 to 1.
In conclusion, the situation that represents a proportional relationship with a unit rate of 4 to 1 is the first situation: A tire warehouse has exactly 12,800 automobile tires for 3,200 automobiles.