Jason is making punch by mixing 1/2 of a cup of orange juice and 1/5 of a cup of mango juice. He wants to mix the orange juice and mango juice in the same ratio to make 21 cups of punch. Use the table to determine how many cups of orange juice and mango juice he will need.
To find the total amount of orange juice needed, multiply 1/2 cup by the number of parts in the ratio. Since the total number of parts is 1 + 1/5 = 6/5, the amount of orange juice needed is 1/2 x 6/5 = 6/10 = 3/5 cup.
To find the total amount of mango juice needed, multiply 1/5 cup by the number of parts in the ratio. The amount of mango juice needed is 1/5 x 6/5 = 6/25 cup.
To find how many cups of each juice are needed if the total amount of punch is 21 cups, divide the total amount of the juice by the total number of parts in the ratio:
For the orange juice: (3/5 cup) / (6/5 parts) = (3/5) / (6/5) = (3/5) * (5/6) = 3/6 = 1/2 cup.
For the mango juice: (6/25 cup) / (6/5 parts) = (6/25) / (6/5) = (6/25) * (5/6) = 30/150 = 1/5 cup.
Therefore, Jason will need 1/2 cup of orange juice and 1/5 cup of mango juice to make 21 cups of punch.
The table can be as follows:
| Juice | Part | Cups |
|------------|--------------|------|
| Orange | 1 | 10 |
| Mango | 1/5 | 4 |
|**Total** |6/5 | 14 |