Question

A fruit punch is made by mixing grape juice and apple juice in the ratio of 4 to 2. How many glasses of grape juice and apple juice are needed to make 36 glasses of fruit punch?


A.
6 glasses of grape juice, 30 glasses of apple juice
B.
12 glasses of grape juice, 24 glasses of apple juice
C.
12 glasses of grape juice, 6 glasses of apple juice
D.
24 glasses of grape juice, 12 glasses of apple juice

Answer 1

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:

1. Calculate the total amount of each part:
\[
\text{One part} = \frac{36 \text{ glasses}}{6 \text{ parts}} = 6 \text{ glasses per part}
\]

2. 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**.