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Math Help - I need help!!

  1. #1
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    I need help!!

    a store has a cost of goods of 486,000 the expected gross margin is 49.50% operating expenses are 225,000 what will be the percent profit?
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  2. #2
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    Gross Profit Margin = (Sales - Cost of Goods Sold) / Sales

    We need to know sales, while we already know CoGS and the GPM. Thus, Sales becomes x in the equation above and we solve for it.

    49.50% = ( x - $486,000)/ x
    x = $ 962,376.24 = Sales

    Net Profit Margin = Net Income / Sales
    Net Income = Sales - Expenses

    Where expenses include operating exp and CoGS.

    So, we now have all the pieces to plug in:
    NPM = ($962,376.24 - $486,000 - $225,000)/$962,376.24
    NPM = $251,376.24/$962,376.24
    NPM = 26.12%

    Be careful when dealing with Net Profit and Net Profit Margin. Net Profit Margin is expressed as a percent, as seen above, while Net Profit is the actual dollar amount of profit ($251,376.24 in this problem). A good way to check if you're in the ballpark on this type of problem is to know that Gross Profit Margin is greater than Net Profit Margin. 26.12% is less than 49.50% so it's likely that we're on the right track.

    ~TC
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  3. #3
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    another question...

    that helps alot thank you. but i have one more question can you give me the step by step in the equation 49.5% =( x-486000)/x

    im having trouble coming up with the number you got.
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  4. #4
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    Our initial equation:
    49.50% = ( x - $486,000)/ x

    Rewrite without the percent:
    .495 = ( x - $486,000)/ x

    Multiply both sides by x:
    .495x = x - $486,000

    Subtract x from both sides:
    (.495x - x) = -$486,000
    -.505x = -$486,000

    Divide both sides by -.505:
    x = $962,376.2376

    And of course, I just rounded to the nearest cent:
    x = $962,376.24

    There ya go!
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  5. #5
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    another

    how do you subtract x from both sides and get -.505?
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  6. #6
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    The coefficient in front of the x on the left is .495 while the coefficient in front of the x on the right is implied as 1. Below, I show it as if you were to factor out x, subtract the one, then multiply the result by x.

    Subtract x from both sides:
    (.495x - 1x) = -$486,000
    x(.495 - 1) = -$486,000
    x(-.505) = -$486,000
    -.505x = -$486,000

    Another way to think of it is that you have .495 x's and you need to subtract from that one x. Which results in a x in the amount of -.505.
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