SOLUTION: Tong and Phillip are working as counselors in a day camp for kids. One of their tasks is to prepare lemonade for snack break. In the camp's recipe box they find three recipes for m

Question 1103253: Tong and Phillip are working as counselors in a day camp for kids. One of their tasks is to prepare lemonade for snack break. In the camp's recipe box they find three recipes for making lemonade from concentrate:
Recipe A: 2 cups concentrate 3 cups cold water
Recipe B: 4 cups concentrate 8 cups cold water
Recipe C: 3 cups concentrate 5 cups cold water
Which recipe will make juice that is the most lemony tasting? Explain in detail how you decided.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
ratio of lemon concentrate to liquid for all of the options is shown below:

Recipe A: 2 cups concentrate 3 cups cold water = 2/3
Recipe B: 4 cups concentrate 8 cups cold water = 4/8
Recipe C: 3 cups concentrate 5 cups cold water = 3/5

you want to compare the ratios to see which one gives you the highest ratio of concentrate to water.

that one should taste the most lemony.

4/8 is 50%.
3/5 is 60%.
2/3 is 66.67%

recipe A has the highest ratio, therefore will probably taste the most lemony.

if you want to do it by fractions, then find the common denominator and compare them that way.

you should simplify the fractions first.

2/3 is already simplified.
4/8 can be simplified to 1/2.
3/5 is already simplified.

your common denominator should include factors of 2, 3, and 5.

a common denominator of 30 should do it.

2/3 * 1/10 = 20/30
1/2 * 15/15 = 15/30
3/5 * 6/6 = 18/30

the one with the most concentrate per volume of mixture is recipe A.

you did it by ratio of concentrate to water.

you can also do it by percentage of concentrate in the mixture.

2 cups concentrate and 3 cups water = 5 cups mixture, of which 2 cups is concentrate.

ratio of concentrate to mixture is 2/5 = 40%

4 cups concentrate and 8 cups water = 12 cups mixture, of which 4 cups is concentrate.

ratio of concentrate to mixture is 4/12 = 1/3 = 33.33%.

3 cups concentrate and 5 cups water = 8 cups mixture, of which 3 cups is concentrate.

ratio of concentrate to mixture is 3/8 = 37.5%.

recipe A is still the winner since it has a higher ratio of concentrate to total mixture.

as such, it should taste more lemony than the others.

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