SOLUTION: how many ml of pure alcohol and how many ml of 4% alcohol solution must be combined to make up 480 ml of an 8% alcohol solution?

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Question 1169472: how many ml of pure alcohol and how many ml of 4% alcohol solution must be combined to make up 480 ml of an 8% alcohol solution?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
How many liters, v of the pure alcohol to add or use?



Solve for v.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

 We have    x    mL of the 8% solution, and

       (480 - x) mL of the pure alcohol. 



x mL of the 8% solution contribute 0.08x mL of the pure alcohol to the new mixture

(480-x) ml of the pure alcohol contribute (480-x) mL of the pure alcohol to the new mixture.



Now we write the balance equation for the pure alcohol

    0.04x + (480-x) = 0.08*480  milliliters


saying that the amount of the pure alcohol in ingredients (left side)
is the same as the amount of the pure alcohol in the final 8% solution (right side).



From the equation

    x =  = 460.



ANSWER.  460 mL of the 4% solution, and the rest, 480 mL - 460 mL = 20 mL of the pure alcohol should be mixed.

Solved.

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In this site, there is entire bunch of lessons covering various types of mixture problems
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts
    - Word problems on mixtures for dry substances like candies, dried fruits
    - Word problems on mixtures for dry substances like soil and sand
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive
    - Advanced mixture problems
    - Advanced mixture problem for three alloys
    - Unusual word problem on mixtures
    - Check if you know the basics of mixtures from Science

    - Special type mixture problems on DILUTION adding water
    - Increasing concentration of an acid solution by adding pure acid
    - Draining-replacing mixture problems
    - How much water must be evaporated
    - Advanced problems on draining and replacing

    - OVERVIEW of lessons on word problems for mixtures


A convenient place to quickly observe these lessons from a  "bird flight height"  (a top view)  is the last lesson in the list.

Read them and become an expert in solution the 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 online textbook 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.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Here is a quick and easy alternative to the standard algebraic solution method shown by the other tutors. It can be used on any of a wide number of different types of 2-part mixture problems.

Picture the problem as starting with some 4% alcohol and adding some 100% alcohol, stopping when the mixture is 8% alcohol.

In stopping at 8%, what fraction of the way from 4% to 100% did you go?

Picturing the three percentages on a number line, observe that 8 is 4/96 = 1/24 of the way from 4 to 100.

That means 1/24 of the total mixture is the 100% alcohol.

ANSWER: 1/24 of the total 480ml, or 20ml, is the 100% alcohol; the other 460ml is the 4% alcohol.

CHECK:
20(1.00)+460(0.04) = 20+18.4 = 38.4
480(0.08) = 38.4
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