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How do you solve ratio problems like these?

  1. Sep 23, 2011 #1
    1. The problem statement, all variables and given/known data

    In each of the following the properties of a compound are given. In each case find A:B:C

    1. 1/5 of A, 2/3 of B and the remainder of C.

    2. 3/8 of A with B and C in the ratio 1:2.

    3. A, B and C are mixed according to the ratios A:B= 2:5 and B:C=10:11.

    2. Relevant equations



    3. The attempt at a solution

    I could only solve the 1st one:

    The common denominator is 15 so 15/3*2=10 and 15/5*1=3. That means A and B are in the ratio 3:10.

    15/15-13/15=2/15 so A:B:C are in the ratio of 10:3:2

    Couldn't solve the other two. Please, help. Thanks.
     
  2. jcsd
  3. Sep 23, 2011 #2

    uart

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    Ok in Q2 you know that the remainder (B and C) make up 5/8. Can you show how to split 5/8 in the ratio 1:2?
     
  4. Sep 23, 2011 #3
    Regarding Question 1:

    I think you got the answer right but in the wrong order.

    [itex]A:B:C[/itex]

    [itex]\frac{1}{5}:\frac{2}{3}:\frac{x}{y}[/itex]

    [itex](\frac{3}{15}:\frac{10}{15}:\frac{2}{15})*15[/itex]

    [itex]3:10:2 == A:B:C[/itex]

    Regarding Question 2:
    You need the provided fraction to become large enough that it's remainder is evenly divisible into three parts.

    Regarding Question 3:
    A:B:C is what you're trying to build, so look at the ratios A:B and B:C as puzzle pieces.
    A:B is too small to fit in with B:C, so you simply need to make A:B larger for it to be congruent with B:C
     
    Last edited: Sep 23, 2011
  5. Sep 28, 2011 #4
    Thank you for the answers.
     
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