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 Priya mix with 100 cups of water to make juice that tastes the same as the original recipe?

Answer 1

To find the ratio of concentrate to water in Priya's original recipe, we need to create a common denominator for the fractions involved:

2 ½ = 2 + ½ = 2 + 2/2 = 2 + 4/2 = 2 + 2 = 2 2/2
2 2/2 = 4/2 + 2/2 = 6/2 + 2/2 = 8/2 = 4.

So 2 ½ cups is equal to 4 cups.

Similarly, we can convert Diego's ratio to a common denominator:

1 ⅔ = 1 + ⅔ = 1 + 2/3 = 3/3 + 2/3 = 5/3.
So 1 ⅔ cups is equal to 5/3 cups.

Now we can find the ratio of concentrate to water for Priya's original recipe:
Concentrate to water = 4 cups / ½ cup = 8/1.
So, the ratio of concentrate to water in Priya's original recipe is 8:1.

To make juice that tastes the same as the original recipe with 100 cups of water, Priya would need to mix:
100 cups of water / 1 = 100/1 cups of water.
Since the ratio of concentrate to water is 8:1, Priya would need to mix:
(8/1) x (100/1) = 800/1 = 800 cups of orange juice concentrate.

Therefore, Priya should mix 800 cups of concentrate with 100 cups of water to make juice that tastes the same as the original recipe.