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Math Help - Help me figure out equations.

  1. #1
    Yep
    Yep is offline
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    Help me figure out equations.

    The only thing I need help with is figuring out these equations. :[

    Your grandfather has $303,000 to invest. He has decided to invest all of it by purchasing some shares of stock in each of three companies: a lumber company that sells for $25 per share and has an expected growth of 6.5% per year, a fast food company that sells for $30 per share and has an expected growth of 10% per year and a discount clothing chain that sells for $15 per share and has an expected growth of 12% per year. The total cost of the lumber company shares exceeds the total cost of the clothing chain by $15,000. If the total growth of all the tree is $28,425 for the year, how many shares of each did he buy?


    My equations are...

    Let -
    x = lumber / 25 / 6.5%
    y = food / 30 / 10%
    z = clothing / 15 / 12%

    25x+30y+15z = 303,000
    .065x+.1y+.12z = 28,425
    -x+z = 15,000


    Where did I go wrong? Any help would be greatly appreciated.
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  2. #2
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    .065x+.1y+.12z = 28,425
    This equation is wrong.
    x, y and z are the number of shares. To find the annual profit, you have to multiply the cost of each share to x, y and z.
    So
    0.065*25x+ 0.1*30y+ 0.12*15z = 28,425
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  3. #3
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    Hello, Yep!

    Your grandfather has $303,000 to invest.
    He has decided to invest all of it by purchasing some shares of stock in three companies:
    a lumber company that sells for $25 per share and has an expected growth of 6.5% per year,
    a fast food company that sells for $30 per share and has an expected growth of 10% per year,
    a discount clothing chain that sells for $15 per share and has an expected growth of 12% per year.
    The total cost of the lumber company shares exceeds the total cost of the clothing chain by $15,000.
    If the total growth of all three is $28,425 for the year, how many shares of each did he buy?


    Let -
    x = lumber / 25 / 6.5%
    y = food / 30 / 10%
    z = clothing / 15 / 12%


    My equations are:

    . . 25x+30y+15z \:=\: 303,000
    . . 0.065x+0.1y+0.12z \:=\: 28,425
    . . -x+z \:=\: 15,000 . ← Here!

    Where did I go wrong?

    Note: no mention was made about "profit".


    Lumber is 15,000 more than Clothing: . x \:=\:z + 15,000 \quad\Rightarrow\quad x - z \:=\:15,000

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