Final answer:
Option D, the ratios 21/28 and 12/16, is the correct answer since both ratios simplify to 3/4, making them proportional to each other.
Step-by-step explanation:
The question asks us to identify which two ratios represent quantities that are proportional. To determine if two ratios are proportional, we need to check if the ratios are equivalent when simplified or if we can find a constant of proportionality between them. Here's a step-by-step explanation:
- A. 56/54 and 36/48 - If we simplify these ratios, we get 28/27 and 3/4 respectively. These ratios are not equivalent, so they are not proportional.
- B. 9/10 and 10/9 - These ratios are inverses of each other, not proportional.
- C. 5/7 and 7/14 - Simplifying the second ratio gives us 5/7 and 1/2. Although these are not directly equivalent, there is a constant of proportionality if we multiply the second ratio by 5/5 to arrive at 5/7 and 5/10. After doubling the denominator of the second ratio to match the first, we finally see that both ratios can indeed be equivalent. Therefore, these two ratios represent quantities that are proportional.
- D. 21/28 and 12/16 - When these ratios are simplified, we get 3/4 for both, which means they are equivalent, thus proportional.
However, a close inspection reveals that the multiplication factor applied to the second ratio in option C is inconsistent, and we are left with two different ratios, which means they also are not proportional. Therefore, the correct answer is D. The ratios 21/28 and 12/16, both of which simplify to the same fraction (3/4), are proportional.