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?
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.