Jason is making punch by mixing of a cup of orange juice and 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.
Let x be the amount of orange juice in cups and y be the amount of mango juice in cups.
Given:
- x + y = 21 (total amount of punch)
- x/y = 3/4 (ratio of orange juice to mango juice)
From the second equation:
x = (3/4)y
Substitute x = (3/4)y into the first equation:
(3/4)y + y = 21
(7/4)y = 21
y = 21 * 4 / 7
y = 12 cups
Substitute y = 12 into x = (3/4)y:
x = (3/4) * 12
x = 9 cups
Therefore, Jason will need 9 cups of orange juice and 12 cups of mango juice to make 21 cups of punch.