A proportional relationship is a relationship between equivalent ratios. Imagine that ice cream costs $2 per scoop. If you get one scoop of ice cream, you’ll pay $2. If you get two scoops, you’ll pay $4, and for three scoops you’ll pay $6.
These ratios of scoops to prices are equivalent. Therefore, the relationship between number of scoops and total price is proportional. To find out the total price of your ice cream, you can always multiply the number of scoops you’re getting by the same number, 2.
Which of these can be described with a proportional relationship?
A
An athlete runs 1 mile in 7 minutes and another mile in 7.5 minutes.
B
An athlete does 10 push-ups for every 1 mile she runs.
C
An athlete runs 2 miles and does 25 push-ups.
D
An athlete runs 5 miles 3 times a week.
B
An athlete does 10 push-ups for every 1 mile she runs.
The option that can be described with a proportional relationship is option B.
In option B, it is stated that the athlete does 10 push-ups for every 1 mile she runs. This can be represented as a ratio of 10 push-ups to 1 mile. Since this ratio is consistent, it implies a proportional relationship between the number of push-ups and the distance ran.
To determine which of these scenarios can be described with a proportional relationship, we need to see if the ratios involved are equivalent.
Option A states that the athlete runs 1 mile in 7 minutes and another mile in 7.5 minutes. The ratios of miles to time are not equivalent, so this scenario does not represent a proportional relationship.
Option B states that the athlete does 10 push-ups for every 1 mile she runs. Here, the ratio of push-ups to miles is consistent, with a ratio of 10:1. This scenario represents a proportional relationship.
Option C states that the athlete runs 2 miles and does 25 push-ups. The ratio of push-ups to miles is not consistent with the ratio of 10:1 mentioned in option B, so this scenario does not represent a proportional relationship.
Option D states that the athlete runs 5 miles 3 times a week. There is no comparison of ratios in this scenario, so it does not represent a proportional relationship.
Therefore, the only scenario that can be described with a proportional relationship is option B: An athlete does 10 push-ups for every 1 mile she runs.