Final answer:
To make 21 cups of punch while keeping the same proportion of 1/2 cup orange juice to 1/5 cup mango juice, Jason will need 10.5 cups of orange juice and 4.2 cups of mango juice.
Step-by-step explanation:
Jason is making punch by mixing 1/2 of a cup of orange juice and 1/5 of a cup of mango juice in a certain ratio, and he wants to maintain the same ratio to make a total of 21 cups of punch.
To find out how many cups of each juice he'll need, we must first add the initial amounts of the two juices:
1/2 cup + 1/5 cup = 5/10 cup + 2/10 cup = 7/10 cup for the initial mixture.
Next, we will set up a proportion where 7/10 cup corresponds to 21 cups, expressed as 7/10 : 21/x, where x represents the total cups of one type of juice.
By cross-multiplying, we can solve for x. Here's the proportion for orange juice:
(1/2) / (7/10) = x / 21.
Cross-multiplying gives us 10x = 21 * 5, which results in 105/10 = 10.5 cups of orange juice.
Following the same steps for mango juice provides us with 4.2 cups of mango juice.
Therefore, Jason will need 10.5 cups of orange juice and 4.2 cups of mango juice to maintain the proportional mix.