TEAS 7 ExamC++TEAS 7 Math Practice X4BoostTwo friends get frozen yoghurt the ratio of yoghurt to toppings is 43 if one of the friends has 45 oz of toppings in their bowl which of the following is the amount of yoghurt in their desertCurrent
Two friends get frozen yoghurt. The ratio of yoghurt to toppings is 4:3. If one of the friends has 4.5 oz of toppings in their bowl, which of the following is the amount of yoghurt in their desert?
A.
6 oz
B.
5.5 oz
C.
3 oz
D.
3.5 oz
The correct answer and Explanation is :
To solve this problem, we need to apply the concept of ratios.
Given Information:
- The ratio of yoghurt to toppings is 4:3.
- One friend has 4.5 oz of toppings.
We need to find the amount of yoghurt in their dessert based on this ratio.
Step 1: Understanding the Ratio
The ratio of 4:3 means that for every 4 parts of yoghurt, there are 3 parts of toppings. Since the ratio holds true for any amount of yoghurt and toppings, we can use this relationship to solve for the unknown quantity (yoghurt in this case).
Step 2: Setting up the Proportion
Let ( y ) represent the amount of yoghurt in ounces. The proportion based on the ratio can be set up as:
[
\frac{y}{4.5} = \frac{4}{3}
]
Step 3: Solving the Proportion
Now, we solve for ( y ) by cross-multiplying:
[
3y = 4 \times 4.5
]
This simplifies to:
[
3y = 18
]
Now, divide both sides by 3 to isolate ( y ):
[
y = \frac{18}{3} = 6
]
Step 4: Conclusion
The amount of yoghurt in the dessert is 6 ounces.
Explanation
This problem uses a basic ratio and proportion concept. We know that the ratio of yoghurt to toppings is 4:3, meaning that for every 3 parts of toppings, there are 4 parts of yoghurt. By setting up a proportion with the given amount of toppings (4.5 oz), we were able to calculate the amount of yoghurt.
The correct answer is A. 6 oz.
This method is essential in solving problems involving ratios, where a known part is used to determine an unknown quantity based on a given relationship.