19. 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?

Answer: A

Explanation:

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

There are 5 boxes with a prize and 15 boxes without a prize, resulting in a ratio of 5 to 15, which simplifies to 1 to 3.

A) 1:03

This option is correct as it accurately represents the ratio of boxes with a prize (5) to boxes without a prize (15). When simplified, the ratio 5:15 reduces to 1:3.

B) 1:04

This option is incorrect because it suggests that for every box with a prize, there are 4 boxes without a prize. However, there are actually 15 boxes without a prize, making this ratio inaccurate.

C) 1:05

This option is also incorrect as it implies that for every box with a prize, there are 5 boxes without a prize. The actual count shows 15 boxes without a prize, which does not support this ratio.

D) 2:03

This option is incorrect as it presents a misleading ratio. It suggests that there are 3 boxes without a prize for every 2 boxes with a prize, which does not reflect the actual counts of 5 prize boxes and 15 non-prize boxes.

Conclusion

The correct answer, 1:3, accurately reflects the relationship between the number of boxes with a prize and those without. All other options fail to represent this relationship correctly, demonstrating a misunderstanding of the basic principles of ratio simplification.