9. Two friends get frozen yogurt. The ratio of yogurt to toppings is 4:3. If one friend has 4.5 oz of toppings in their bowl, what is the amount of yogurt in their dessert?
Answer: A
The amount of yogurt in their dessert is 6 oz.
To find the amount of yogurt, we use the given ratio of yogurt to toppings, which is 4:3. With one friend having 4.5 oz of toppings, we can calculate the corresponding amount of yogurt.
A) 6 oz
This option is correct because if the ratio of yogurt to toppings is 4:3, then for every 4 parts of yogurt, there are 3 parts of toppings. By setting up a proportion, if 3 parts equals 4.5 oz, then 4 parts (the yogurt) can be found using the equation (4/3) * 4.5 oz = 6 oz.
B) 5.5 oz
This option is incorrect. While it is close, 5.5 oz does not maintain the ratio of 4:3 when 4.5 oz of toppings are considered. Using the correct ratio yields a different amount of yogurt.
C) 3 oz
This option is incorrect as well. A yogurt amount of 3 oz would imply a different ratio of yogurt to toppings, specifically a 3:3 ratio, which does not correspond to the original 4:3 ratio provided in the question.
D) 3.5 oz
This option is also incorrect. An amount of 3.5 oz of yogurt does not satisfy the ratio of 4:3 given 4.5 oz of toppings. The correct calculation reveals that 3.5 oz is insufficient to maintain the specified ratio.
Conclusion
The correct answer of 6 oz aligns perfectly with the given ratio of yogurt to toppings, confirming that for every 4.5 oz of toppings, the corresponding yogurt amount is indeed 6 oz. The other options fail to maintain the 4:3 ratio, thereby making them incorrect in the context of the question.