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Math Help - Simultaneous Linear Equations help.

  1. #1
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    Simultaneous Linear Equations help.

    Q1
    An investor received $1400 per annun from a sum of money, with part of it invested at 10% and the remainder at 7% interest. This investor found that if she interchanged the amounts she had invested she could increase her return by $90 per annun. Calculate the total amount invested.


    Q2
    A shopkeeper sold his entire stock of shirts and ties in a sale for $10 000. The hirts were priced at 3 for $100 and the ties $20 each. If he had sold only half the shirts and two-thirds of the ties he would have $6000. How many of each did he sell?

    Any help would be appreciated. I would also like to know how to figure these out step by steps.

    Thank you for reading.
    Last edited by AltQQ; January 28th 2009 at 04:13 PM.
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  2. #2
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    Question 1
    Let x be the amount of money invested with the 10% interest.
    Equation would be (12)(0.1x) + (1400-x)(12)(0.07) = (1400 - x)(12)(0.1) + 12(0.07x)
     1.2x + 1176 - 0.84x = 1680 - 1.2x + 0.84x - 90
     x = 575
    Invested in 10% = $575, invested in 7% - $825

    Question 2
    Let x be the amount of shirts the shopkeeper owns
    Let y be the amount of ties the shopkeeper owns
    Hence, (100)(\frac{x}{3}) + 20y = 10000
    100x + 60y = 30000 - eqn 1
    (100)(\frac{x}{6}) + (\frac{2}{3})(20y) = 6000
    100x + 80y = 36000 - eqn 2
    eqn 2 - eqn 1 = 100x + 80y - 100x - 60y = 36000 - 30000
    20y = 6000
    y = 300, from eqn 1, x = 120
    Last edited by elitewarr; January 28th 2009 at 05:01 AM.
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  3. #3
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    You got the answer for Q2, but not Q1. Thanks anyways.
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