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Math Help - Ratios and proportions

  1. #1
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    Ratios and proportions

    Hi, i am having a little bit of difficulties with ratios and proportions and would really appreciate if someone could help me understand this problem.

    Solve x : 6/8 = 9/x+7

    Alright so here's what i would do :

    8 * 9 = 72 / 6.

    72 divided by 6 = 12

    12 + 7 = 19.

    x = 19.

    Apparently, this is wrong. The correct answer is :

    12 - 7 = 5.

    x = 5.

    My question is, why exactly do you have to subtract 7 instead of adding it?
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Ratios and proportions

    I don't see why you have the step 12 + 7 = 19. You need to carefully work through the steps for solving for x. First let's use parentheses so it's clear what the problem is:

    6/8 = 9/(x+7)

    First you can multiply both sides by 8 to get:

    8 * 6/8 = 8 * 9/(x +7), or 6 = 72/(x+7)

    Note that I use the '*' symbol to mean multiplication, to avoid confusion with the unknown value 'x.'

    Now divide both sides by 6:

    6/6 = (72/6)/(x +7), or 1 = 12/(x+7)

    Now multiply through both sides by (x+7)

    (x+7) * 1 = (x+ 7) * 12/(x+ 7), or x+7 = 12

    Finally subtract 7 from both sides:

    (x+7)-7 = 12 - 7, or x = 5.
    Thanks from jonasjones
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