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
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.