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Math Help - Too thick to solve this problem!!!!

  1. #1
    bonbhoy
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    Question Too thick to solve this problem!!!!

    A housewife buys a certain amount of beef at 4 per kilo and the same amount of sausages at 3 per kilo. If she had split the money she spent equally between the beef and sausages she would have got 2 kilos more. How much did she spend
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  2. #2
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    Quote Originally Posted by bonbhoy
    A housewife buys a certain amount of beef at 4 per kilo and the same amount of sausages at 3 per kilo. If she had split the money she spent equally between the beef and sausages she would have got 2 kilos more. How much did she spend
    It is worded in a confusing sense but I think I understand it. Let x represent the money she spend on sausages. Also x is the money she spend on beef because she spilt the money equally. Since she can buy more sausages then beef (they are less expensive) the difference between them is 2 (because she gets 2 more kilos). Now place that into an equation. If she spends x yen on sausages then she gets \frac{x}{3}kilos because they are worth (3 yen per kilo). Similarily she gets \frac{x}{4} kilos of beef. Thus, their difference is 2:
    \frac{x}{3}-\frac{x}{4}=2
    To solve this you need to find the common denominator. Which is 12, and multiply both sides by 12:
    12\frac{x}{3}-12\frac{x}{4}=12\times 2
    thus,
    4x-3x=24
    thus,
    x=24kg

    Thus, she brought 24 kilos for both of them. Thus, a total of 48 kilograms of meat where brough.
    Last edited by ThePerfectHacker; January 19th 2006 at 05:51 PM.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by bonbhoy
    A housewife buys a certain amount of beef at 4 per kilo and the same amount of sausages at 3 per kilo. If she had split the money she spent equally between the beef and sausages she would have got 2 kilos more. How much did she spend
    Let x denote the mass of beef bought and s be the amount spent.

    Then:

    4x+3x=s

    Now if instead s/2 is spent on beef and also on sausage these
    buy (s/2)/4\ kg of beef and (s/2)/3\ kg of sausage. As the sum
    of these is 2\ kg more than previously we have:

    s/8+s/6 = 2x+2,

    but s=7x so:

    \frac{7x}{8}+\frac{7x}{6}=2x+2,

    which has solution x=48\ kg, or s= 336pounds

    These numbers seem implausibly large given the scenario.

    RonL
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