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anonymous

  • one year ago

PERCENTAGES QUESTION :) Two beakers of equal volume Beaker A contains 30% salt Beaker B contains 10% salt How many ounces of solution A should be added to solution B, so that the resulting solution is 20% salt?

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  1. anonymous
    • one year ago
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    so far, I let x be the amount of solution in Beaker A. then, 30% of that is the amount of salt in A....same for B...

  2. mathstudent55
    • one year ago
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    Let's try 10 liters. 10 liters of A has 3 litres salt. 10 liters of B has 1 litres salt. You end up with 20 liters with 4 litres salt. 4 litres out of 20 litres is 20%

  3. anonymous
    • one year ago
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    Okay, yep, I;m following so far....

  4. mathstudent55
    • one year ago
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    Since the concentration you want is exactly the average of the two concentrations you start with, the same amounts of A and B are used.

  5. anonymous
    • one year ago
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    Oki doki, that makes sense - there might be a problem with the worked solution – its talking about ounces, and I have no information about how many ounced the beakers started out with....

  6. mathstudent55
    • one year ago
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    Use ounces where I used litres.

  7. anonymous
    • one year ago
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    heres the part that dosnt make any sense to me in the worked solution: "the resulting solution will be 50 + x ounces and its concentration of salt will be 20%(50+x)....

  8. anonymous
    • one year ago
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    im guessing instead of your 10L base, theyve used 50 ounces?

  9. mathstudent55
    • one year ago
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    Is there any info missing from the question you posted? Where does the number 50 come from in the solution?

  10. anonymous
    • one year ago
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    thats exactly my problem...

  11. mathstudent55
    • one year ago
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    Beaker A has x ounces of 30% salt solution. Beaker B has x ounces of 10% salt solution. (Both beakers have x amount because we are the beakers have equal volume.)

  12. anonymous
    • one year ago
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    Yes. Corecct

  13. mathstudent55
    • one year ago
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    x ounces of solution B has 0.1x ounces of salt.

  14. anonymous
    • one year ago
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    Yep

  15. mathstudent55
    • one year ago
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    Now we need to start adding solution A to solution B until we have a new solution that is 20% salt.

  16. mathstudent55
    • one year ago
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    Let's say we add y ounces of solution A to solution B.

  17. anonymous
    • one year ago
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    To do that, we need to find the volume in A containing a concentration of 10%?

  18. anonymous
    • one year ago
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    Okay, yep

  19. mathstudent55
    • one year ago
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    y ounces of solution A has 0.3y ounces of salt

  20. anonymous
    • one year ago
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    correct

  21. mathstudent55
    • one year ago
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    We will have a total of salt: 0.3y + 0.1x Ok?

  22. anonymous
    • one year ago
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    Yep, all good so far. Thanks for going through it with me.

  23. mathstudent55
    • one year ago
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    Next, we will have a total amount of solution of: x + y Ok?

  24. anonymous
    • one year ago
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    Yes.

  25. mathstudent55
    • one year ago
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    We want the new solution to have a concentration of 20% salt. 20% = 0.2 That means \(\dfrac{0.3y + 0.1x}{x + y } = 0.2\)

  26. anonymous
    • one year ago
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    Okay, cool.

  27. mathstudent55
    • one year ago
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    Now let's solve that equation and what we get.

  28. anonymous
    • one year ago
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    x=y?

  29. mathstudent55
    • one year ago
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    \(\dfrac{0.3y + 0.1x}{x + y } = 0.2\) \(0.3y + 0.1x = 0.2(x + y)\) \(0.3y + 0.1x = 0.2x + 0.2y\) \(0.1y = 0.1x\) \(y = x\) Correct.

  30. mathstudent55
    • one year ago
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    Since we chose x to be the amount of solution B and y to be the amount of solution A, we see the amounts must be the same no matter how much each beaker has.

  31. anonymous
    • one year ago
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    Understood

  32. mathstudent55
    • one year ago
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    Great.

  33. anonymous
    • one year ago
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    So do you think that they made x=y=50 ounces?

  34. anonymous
    • one year ago
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    in the solutions?

  35. mathstudent55
    • one year ago
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    That's what I am thinking.

  36. anonymous
    • one year ago
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    Yeah, okay. Well thanks for going through it with me in detail. Appreciate your work :)

  37. mathstudent55
    • one year ago
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    Before the part of the solution you quoted above mentioning 50 + x, was there any mention of 50?

  38. mathstudent55
    • one year ago
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    You're welcome.

  39. anonymous
    • one year ago
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    their equation is exactly what you had, except they made 50=y for some reason: 10%50 + 30%x = 20%(50+x) I understand the equation now, thank you. And no. No mention anywhere of 50 :(

  40. anonymous
    • one year ago
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    Also, just wondering if you know how to change the username on open study? i can find the change passwords under settings, but is it even possible to change usernames?

  41. mathstudent55
    • one year ago
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    I guess they just assumed they would use 50 ounces of one solution, and then they found how many ounces of the other solution they needed. It turns out to be 50, of course, bec now we know it's the same amount of both solutions.

  42. mathstudent55
    • one year ago
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    I don't know if you can change username in OS.

  43. anonymous
    • one year ago
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    Yes, I reckon you're right on that one. Okay then, thank you!

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