Priya mixes 2 ½ cups of water with ⅓ cup of orange juice concentrate. Diego mixes 1 ⅔ cups of water with ¼ cup orange juice concentrate.

Question

How much concentrate should Diego mix with 100 cups of water to make juice that tastes the same as the original recipe?

Answer 1

To find the amount of concentrate that Diego should mix with 100 cups of water, we can set up a proportion:

(1 ⅔ cups of water) / (¼ cups of concentrate) = (100 cups of water) / (x cups of concentrate)

First, we need to convert both mixed numbers into improper fractions:

1 ⅔ = (3/3 + 2/3) = 5/3
2 ½ = (2/2 + 1/2) = 5/2

Now we can substitute these values into our proportion:

(5/3 cups of water) / (1/4 cups of concentrate) = (100 cups of water) / (x cups of concentrate)

To solve for x, we can cross-multiply:

(5/3) * x = (100) * (1/4)
5x/3 = 100/4

Next, we can simplify the right side of the equation:

5x/3 = 25
5x = 75
x= 75/5
x = 15

So Diego should mix 15 cups of orange juice concentrate with 100 cups of water in order to make juice that tastes the same as the original recipe.