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Math Help - Using Ratio to Solve this

  1. #1
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    Using Ratio to Solve this

    A certain mixture X consists of ingredients A, B and C in the ration of 1:4:7 by weight.
    Another mixture Y consists of ingredients A, B and C in the ration of 2:5:8 by weight.
    If equal amount of X and Y are mixed together, find the ratio of the ingredients A, B and C in the new mixture.
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  2. #2
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    Re: Using Ratio to Solve this

    Well, each 12 kg of X contain 1 kg of A, 4 kg of B and 7 kg of C, and each 15 kg of Y contain 2 kg of A, 5 kg of B and 8 kg of C. If we mix 12 kg of X and 15 kg of Y, this would not be equal amounts. Do you have an idea how to come up with equal amount of X and Y without needing to consider fractions of 1 kg?
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  3. #3
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    Re: Using Ratio to Solve this

    Quote Originally Posted by KCMH View Post
    A certain mixture X consists of ingredients A, B and C in the ration of 1:4:7 by weight.
    Another mixture Y consists of ingredients A, B and C in the ration of 2:5:8 by weight.
    If equal amount of X and Y are mixed together, find the ratio of the ingredients A, B and C in the new mixture.
    For every kg of mixture X, the ingredients are in the ratio 1 : 4 : 7, so mixture X consists of (1/12)kg of A, (4/12)kg of B, and (7/12)kg of C.

    For every kg of mixture Y, the ingredients are in the ratio 2 : 5 : 8, so mixture Y consists of (2/15)kg of A, (5/15)kg of B, and (8/15)kg of C.

    Therefore, when the two mixtures are added together, every 2kg of mixture X + Y will have

    (1/12)kg + (2/15)kg of mixture A
    = (5/60)kg + (8/60)kg of mixture A
    = (13/60)kg of mixture A.

    (4/12)kg + (5/15)kg of mixture B
    = (20/60)kg + (20/60)kg of mixture B
    = (40/60)kg of mixture B.

    (7/12)kg + (8/15)kg of mixture C
    = (35/60)kg + (32/60)kg of mixture C
    = (67/60)kg of mixture C.


    But this is for every 2kg of mixture X + Y. For every 1kg, we will need to halve each of the results.

    So in every kg of X + Y, there will be (13/120)kg of A, (40/120)kg of B, (67/120)kg of C.

    Therefore the ratio of A : B : C in the combined mixture is 13 : 40 : 67.
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    Re: Using Ratio to Solve this

    Quote Originally Posted by Prove It View Post
    For every kg of mixture X, the ingredients are in the ratio 1 : 4 : 7, so mixture X consists of (1/12)kg of A, (4/12)kg of B, and (7/12)kg of C.

    For every kg of mixture Y, the ingredients are in the ratio 2 : 5 : 8, so mixture Y consists of (2/15)kg of A, (5/15)kg of B, and (8/15)kg of C.

    Therefore, when the two mixtures are added together, every 2kg of mixture X + Y will have

    (1/12)kg + (2/15)kg of mixture A
    = (5/60)kg + (8/60)kg of mixture A
    = (13/60)kg of mixture A.

    (4/12)kg + (5/15)kg of mixture B
    = (20/60)kg + (20/60)kg of mixture B
    = (40/60)kg of mixture B.

    (7/12)kg + (8/15)kg of mixture C
    = (35/60)kg + (32/60)kg of mixture C
    = (67/60)kg of mixture C.


    But this is for every 2kg of mixture X + Y. For every 1kg, we will need to halve each of the results.

    So in every kg of X + Y, there will be (13/120)kg of A, (40/120)kg of B, (67/120)kg of C.

    Therefore the ratio of A : B : C in the combined mixture is 13 : 40 : 67.
    Thank you very much.
    I thought of another approach.
    By finding the LCM which is 60.

    Let N be unknown.
    Therefore, for mixture X, we have 1N + 4N + 7N = 60
    N will be = 5
    So Mixture X will be 5:20:35

    Let M be unknown
    Therefore, for mixture Y 2M + 5M + 8M = 60
    M will be = 4
    So Mixture Y will be 8:20:32

    So when Mixture X and Y add up will gives us 13:40:67.
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  5. #5
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    Re: Using Ratio to Solve this

    Yes, this is the way I suggested. But you can take any amount of X and Y as long as it is the same amount (as the problem statement stipulates): whether it is 60 kg or 1 kg; then calculate the amount of A, B, C in each of X and Y, add the amounts of A, B, C pairwise, and you get the ratios.
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