Clare mixes 2\frac{1}{2} cups of water with \frac{1}{3} cup of orange juice concentrate. Han mixes 1\frac{2}{3} cups of water with \frac{1}{4} cup of orange juice concentrate.

Whose orange juice mixture tastes stronger? Explain or show your reasoning.

Han's Orange Juice

Step-by-step explanation:

Clare: 2 1/2 cups water and 1/3 cups concentrate

Han: 1 2/3 cups water and 1/4 cups concentrate

The way to solve this is to make one of the variables is by using the total:

Clare:

2 1/2 + 1/3 = 5/2 + 1/3 = 15/6 + 2/6 = 17/6 cup

(2/6)/(17/6) = (2/6)(6/17) = 2/17 (two parts in 17), or 11.8%

Han:

1 2/3 + 1/4 = 5/3 + 1/4 = 20/12 + 3/12 = 23/12 cup

(3/12)/(23/12) = (3/12)(12/23) = 3/23 (three parts in 23), or 13.04%

We can see Han's orange juice has more concentrate (the higher percentage).

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