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