SOLUTION: If you have 1.75L of an 18% alcohol solution, how much pure alcohol must you add in order to increase the concentration to 60%?

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Question 1124590: If you have 1.75L of an 18% alcohol solution, how much pure alcohol must you add in order to increase the concentration to 60%?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
highlight_green%28highlight_green%28%281.75%2A18%2B100x%29%2F%28x%2B1.75%29=60%29%29
-
1.75%2A18%2B100x=60%28x%2B1.75%29
100x%2B1.75%2A18=60x%2B60%2A1.75
40x=60%2A1.75-18%2A1.75
40x=42%2A1.75
x=%2842%2A1.75%29%2F40
highlight%28x=1.8375%29literspurealcohol
Best to call it 1.84 L according to the number values given.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Your equation is


    %280.18%2A1.75+%2B+A%29%2F%281.75%2BA%29 = 0.6,   


where A is the amount of the pure alcohol to add.


    0.18*1.75 + A = 0.6*(1.75 + A)


    A - 0.6*A = 0.6*1.75 - 0.18*1.75


    A = %280.6%2A1.75+-+0.18%2A1.75%29%2F%281-0.6%29 = 1.8375 liters of pure alcohol to add.


Check.  %280.18%2A1.75+%2B+1.8375%29%2F%281.75%2B1.8375%29 = 0.6.   ! Correct !


Answer.  1.8375 liters of pure alcohol to add.

Solved.

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It is a standard and typical mixture problem.

For introductory lessons covering various types of mixture word problems see
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Typical word problems on mixtures from the archive
in this site.

You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization,  from very detailed to very short.

Read them and become an expert in solution mixture word problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook in the section "Word problems" under the topic "Mixture problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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Be aware :   the solution and the answer by  @josgaritmetic are   T O T A L L Y   W R O N G.

For your safety, simply ignore it !


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Comment from student : But josarfthmetic got the same answer? anyway thanks
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My response : Yes, he got the correct answer by fixing his errors after my notice.