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anonymous

  • one year ago

a flask contains 160 milliliters of solution that is 25% alcohol by volume. How much pure alcohol must be added to the flask so that the resulting solution is 60% alcohol by volume?

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  1. phi
    • one year ago
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    160 milliliters of solution that is 25% alcohol by volume. First, how many ml of alcohol do we have ?

  2. anonymous
    • one year ago
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    we have 40

  3. anonymous
    • one year ago
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    120 of the remainder

  4. anonymous
    • one year ago
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    i don't understand why it's not 56

  5. phi
    • one year ago
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    ok. now let's add an unknown "x" amount of alcohol, so that we have 40+ x ml of alcohol of course, we have to pour the x ml of alcohol into the mixture so the mixture has 160+x ml

  6. anonymous
    • one year ago
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    160*.6=96-40= 56

  7. phi
    • one year ago
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    next , we use this fact: resulting solution is 60% alcohol by volume in other words, the amount of alcohol will be 0.6(160+x) and that has to equal 40+x in other words, the equation is 0.6(160+x) = 40 + x now we use algebra to solve for x (amount of alcohol to add)

  8. anonymous
    • one year ago
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    why is it 160+x ? sin't 160 the total amount of the solution?

  9. anonymous
    • one year ago
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    isnt*

  10. phi
    • one year ago
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    we start with 160 (which is 40 alcohol and 120 water?) unfortunately it is all mixed together. But if we add pure alcohol, the percent of alcohol goes up. For example if we add lots and lots of alcohol, the mixture becomes more alcohol. so pour in x of pure alcohol into the mixture we have 160+x ml total now

  11. phi
    • one year ago
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    now take 60% of the new amount

  12. anonymous
    • one year ago
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    OHHHHHHHHHHHHHHH

  13. phi
    • one year ago
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    0.6(160+x) = amount of pure alcohol the amount of alcohol will be 40 (the amount in the original) + x (the amount we added) 0.6(160+x) = x+ 40 the thinking might be confusing, but if you see it, it is quite nice.

  14. phi
    • one year ago
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    can you solve it?

  15. anonymous
    • one year ago
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    sorry i hadda help my dad with some tools

  16. anonymous
    • one year ago
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    140

  17. anonymous
    • one year ago
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    thank u so much phi!

  18. phi
    • one year ago
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    Let's see if it makes sense. The new mixture has 160+140= 300 ml of liquid we know we have 40 ml of alcohol (from the original 160) and we add 140 ml of alcohol so it has 40+140= 180 ml of alcohol if we did it right, 180/300 should be 60%

  19. anonymous
    • one year ago
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    Yes it works out

  20. phi
    • one year ago
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    and 180/300 is 60/100 = 60% so it looks good.

  21. anonymous
    • one year ago
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    thank you <333333

  22. phi
    • one year ago
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    Now that the answer makes sense, review your thinking about how to do it. And try to remember what confused you. That is what I do to try to learn the idea.

  23. anonymous
    • one year ago
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    Yes Yes will do =)

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