There are 20 boxes of cereal on a store shelf, and exactly 5 of these boxes have a prize. What is the ratio of the number of boxes with a prize to the number of boxes without a prize?

Rationale

The ratio of the number of boxes with a prize to the number of boxes without a prize is 1:3.

There are 20 boxes of cereal in total, and since 5 of them have a prize, the number of boxes without a prize is 20 - 5 = 15. Thus, the ratio of boxes with a prize (5) to boxes without a prize (15) simplifies to 1:3.

A (1:03) CORRECT

This choice correctly reflects the simplified ratio of boxes with a prize to those without. With 5 boxes having a prize and 15 boxes lacking one, the ratio can be expressed as 5:15, which simplifies to 1:3 after dividing both sides by 5.

B (1:04) YOUR ANSWER

This choice incorrectly suggests that for every box with a prize, there are four boxes without. However, this calculation does not match the actual numbers, as there are 15 boxes without a prize, not 20, making the ratio incorrect.

C (1:05) YOUR ANSWER

This choice implies a ratio where for every box with a prize, there are five boxes without. Since there are 15 boxes without a prize, this ratio is also incorrect. The correct ratio is 1:3, not 1:5.

D (2:03) YOUR ANSWER

This choice suggests a ratio of 2 boxes with a prize for every 3 boxes without. Since there are 5 boxes with a prize and 15 without, this does not accurately represent the relationship and therefore is incorrect.

Conclusion

The ratio of boxes with a prize to boxes without is fundamental in understanding the distribution of prizes among the cereal boxes. The correct ratio of 1:3 clearly indicates that for every box with a prize, there are three boxes without, which aligns with the total of 20 boxes on the shelf. Understanding ratios like this helps in analyzing proportions in various contexts.

There are 20 boxes of cereal on a store shelf, and exactly 5 of these boxes have a prize. What is the ratio of the number of boxes with a prize to the number of boxes without a prize?

The ratio of the number of boxes with a prize to the number of boxes without a prize is 1:3.

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