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?
If necessary round your answer to the nearest hundredth
To find out how much concentrate Priya should mix with 100 cups of water, we can set up a proportion.
First, we need to find the ratio of water to concentrate in the original recipe for both Priya and Diego.
For Priya:
2 ½ cups water : ⅓ cup concentrate
For Diego:
1 ⅔ cups water : ¼ cup concentrate
Now, we can set up the proportion using the ratio obtained for Priya and our unknown variable x:
2.5 cups water / (1/3) cup concentrate = 100 cups water / x cups concentrate
Simplifying the proportion, we have:
2.5 / (1/3) = 100 / x
Multiplying both sides of the equation by (1/3) and dividing both sides by 2.5, we get:
x = (100/2.5) * (1/3) = 40/1 * 1/3 = 40/3 = 13.33
Therefore, Priya should mix 13.33 cups of concentrate with 100 cups of water to make juice that tastes the same as the original recipe. Rounded to the nearest hundredth, the answer is 13.33 cups.