To determine how many glasses of grape juice and apple juice are needed to make 36 glasses of fruit punch in the ratio of 4 to 2, we first need to find the total parts of the mixture.
The ratio of grape juice to apple juice is 4:2, which can be simplified to 2:1. This means for every 3 parts of the mixture (2 parts of grape juice + 1 part of apple juice), 2 parts are grape juice and 1 part is apple juice.
Now let's calculate how many parts are in 36 glasses of fruit punch:
Total parts = 4 (grape juice) + 2 (apple juice) = 6 parts.
To find the amount of each juice, we can use the following calculations:
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Calculate the total amount of each part: \[ \text{One part} = \frac{36 \text{ glasses}}{6 \text{ parts}} = 6 \text{ glasses per part} \]
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Now we can calculate the amount of grape juice and apple juice:
- Grape juice: \( 4 \text{ parts} \times 6 \text{ glasses/part} = 24 \text{ glasses} \)
- Apple juice: \( 2 \text{ parts} \times 6 \text{ glasses/part} = 12 \text{ glasses} \)
So, to make 36 glasses of fruit punch, we need:
- 24 glasses of grape juice
- 12 glasses of apple juice
The correct answer is: D. 24 glasses of grape juice, 12 glasses of apple juice.
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