SOLUTION: I have a gallon of lemonade that is 20% lemon juice. I like it better when it is 25% juice. How much juice should I add? I know that I need to add 5% more lemon juice, so do I n

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: I have a gallon of lemonade that is 20% lemon juice. I like it better when it is 25% juice. How much juice should I add? I know that I need to add 5% more lemon juice, so do I n      Log On


   

Question 710520: I have a gallon of lemonade that is 20% lemon juice. I like it better when it is 25% juice. How much juice should I add?
I know that I need to add 5% more lemon juice, so do I need to just figure out how to say 5/100 gallons? ... Like in quarts or something?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A lemonade that is 25% lemon juice would have
25%2F100=0.25 gallons of lemon juice in
exactly 1 gallon of lemonade.
A lemonade that is 20% lemon juice has
20%2F100=0.20 gallons of lemon juice in
exactly 1 gallon of lemonade.
If you add 5%2F100 gallon lemon juice, you will have a total of
1%265%2F100 gallons = 1.05 gallons of lemonade containing 20%2F100%2B5%2F100=25%2F100 or 0.20%2B0.05=0.25 gallons of lemon juice.
That will not be exactly 25% lemon juice.
In fact, the percentage is %280.25%2F1.05%29%2A100% = about 23.8%
x = gallons of lemon juice to add
1%2Bx = final volume of lemonade (in gallons)
1%2A0.20 = gallons of lemon juice in original 1 gallon of lemonade
%281%2Bx%29%2A0.25 = gallons of lemon juice in final mixture
1%2A0.20%2Bx=%281%2Bx%29%2A0.25
0.20%2Bx=0.25%2B0.25x
0.20%2Bx-0.25x=0.25
x-0.25x=0.25-0.20
0.75x=0.05 --> 0.75x%2F0.75=0.05%2F0.75 --> highlight%28x=1%2F15%29 = approx. 0.0633 gallons.
The number does not get prettier in quarts:
1%2F15gallon = 4%2F15quarts