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).

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.