Final answer:
Pairs of ratios are proportional if they can form a true proportion, meaning their cross products are equal. After comparing each pair, the pairs B (27 to 81 and 21 to 72) and D (40 to 48 and 100 to 120) are found to be proportional.
Step-by-step explanation:
To determine which pairs of ratios represent quantities that are proportional, we must compare the ratios to see if they can form a true proportion when they are set equal to each other. Proportions occur when two ratios are equivalent. We can test each pair by checking if the cross products are equal, which is the defining property of a proportional relationship.
- A. 30 to 36 and 48 to 46 - These are not proportional because 30 * 46 is not equal to 48 * 36.
- B. 27 to 81 and 21 to 72 - These are proportional because when reduced, both ratios become 1 to 3 (27/81 = 1/3 and 21/72 = 1/3).
- C. 4 to 9 and 14 to 14 - These are not proportional because 4 * 14 is not equal to 9 * 14.
- D. 40 to 48 and 100 to 120 - These are proportional because when reduced, both ratios become 5 to 6 (40/48 = 5/6 and 100/120 = 5/6).
Therefore, the pairs that represent proportional quantities are Option B (27 to 81 and 21 to 72) and Option D (40 to 48 and 100 to 120).