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Math Help - How to find the greater part of the following equation

  1. #1
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    How to find the greater part of the following equation

    184 is divided into two parts such that one-third of one part may exceed one-seventh of the other part by 8, then the greater part is _______.

    The possible answers are 72, 110, 112, 114.

    I have tried this question in several ways, but I am unable to solve this question. Can someone point me in the right direction.
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  2. #2
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    Re: How to find the greater part of the following equation

    You have to solve following system of equations :

    x+y=184

    \frac{1}{3}\cdot x= \frac{1}{7} \cdot y + 8
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  3. #3
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    Re: How to find the greater part of the following equation

    thanks that helps.
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  4. #4
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    Re: How to find the greater part of the following equation

    I'll continue where princeps ended his reply.

    x + y = 184..........Equation A
    (x/3) = (y/7) + 8...Equation B

    I will solve Equation A for either x or y. How about for y?

    x + y = 184

    y = 184 - x

    I will now plug that for y in Equation B to find the value of x.

    (x/3) = [(184 - x)/7)] + 8

    Multiply by 21 to clear the fractions on both sides of the equation.

    After doing so, we get

    7x = 3(184 - x) + 8(21)

    7x = 552 - 3x + 168

    7x = -3x + 720

    7x + 3x = 720

    10x = 720

    x = 720/10

    x = 72

    Let x = 72 in either Equation A or B above.

    I will use Equation A.

    x + y = 184

    72 + y = 184

    y = 184 - 72

    y = 112


    Which is the answer? Can you tell me given the amount of work that was done?
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