Question 1161919: 3. What if the desired final mixture was changed to yield a 35% mixture containing pure lemon juice?
a. How many gallons of a 20% solution should be mixed with 15 gallons of a 70% solution to yield a final mixture of lemonade containing 35% of pure lemon juice? Write your answer in complete sentences. Show all work.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! ------------------------------------------------------------------------
3. What if the desired final mixture was changed to yield a 35% mixture containing pure lemon juice?
a. How many gallons of a 20% solution should be mixed with 15 gallons of a 70% solution to yield a final mixture of lemonade containing 35% of pure lemon juice? Write your answer in complete sentences.
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Two "juice" concentrations to start with: 20% and 70%.
Given, 15 gallons of the 70%;
How much of the 20% to produce mix of 35%?
Lemon content of the parts = lemon content of the whole mix
Simplify and solve.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
"Write your answer in complete sentences. Show all work."
There is no sense in writing that in your post; that is your job, not ours. We only show you how to solve the problem -- or how to set it up to be solved.
(1) With formal algebra....
70% of the 15 gallons you start with, plus 20% of the x gallons you are adding, equals 35% of the (x+15) gallons of the final mixture:
Solve using basic algebra, although the numbers are not particularly "nice"....
(2) A completely different solution method, which will get you to the answer to any "mixture" problem like this much faster, and with far less effort, then the traditional formal algebraic method.
You are starting with 70% solution and adding 20% solution, ending with 35% solution.
Model that by thinking of walking along a number line from 70 to 20, stopping when you get to 35.
What fraction of the distance have you gone when you stop? 70 to 20 is a distance of 50; 70 to 35 is a distance of 35. You have gone 35/50 = 7/10 of the distance.
That means 7/10 of the mixture is what you are adding.
So the 15 gallons you started with is 3/10 of the final mixture; that means the 7/10 of the final mixture that you added is 35 gallons.
ANSWER: 35 gallons
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