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Math Help - making correct linear equation

  1. #1
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    making correct linear equation

    this problem is hurting me. It's from the National University of Colombia 2007 entrance exam (translated from Spanish), and I need to understand it's principles for their test in two days.

    When one adds a hard drive to a new personal computer, the new system costs $2900 x 10^3. One knows that 1/3 of the computer, plus 1/5 of the hard drive adds up to $870 x 10^3. If x represents the value of the computer and y the hard drive, a system of linear equations that permits calculating the value of the hard drive is:

    A.
    x - y = 290 x 10^4
    5x + 3y = 1305 x 10^4

    B.
    x+y=290 x 10^4
    3x + 5y = 87 x 10^4

    C.
    x - y = 290 x 10^4
    5x + 3y = 87 x 10^4

    D.
    x + y = 290 x 10^4
    5x + 3y = 1305 x 10^4

    The answer is D, but I'm not sure why. Please explain it if you can. Thank you
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  2. #2
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    Quote Originally Posted by mpoderoso View Post
    this problem is hurting me. It's from the National University of Colombia 2007 entrance exam (translated from Spanish), and I need to understand it's principles for their test in two days.

    When one adds a hard drive to a new personal computer, the new system costs $2900 x 10^3. One knows that 1/3 of the computer, plus 1/5 of the hard drive adds up to $870 x 10^3. If x represents the value of the computer and y the hard drive, a system of linear equations that permits calculating the value of the hard drive is:

    A.
    x - y = 290 x 10^4
    5x + 3y = 1305 x 10^4

    B.
    x+y=290 x 10^4
    3x + 5y = 87 x 10^4

    C.
    x - y = 290 x 10^4
    5x + 3y = 87 x 10^4

    D.
    x + y = 290 x 10^4
    5x + 3y = 1305 x 10^4

    The answer is D, but I'm not sure why. Please explain it if you can. Thank you
    D is correct as obviously a computer (x) plus a hard drive (y) = 2900 X 10 ^3 therefore x + y = 290\times 10^4

    Now one thrid of the computer plus one fifth of the hard drive costs 870X10^3.

    The equation is

    \frac{1}{3}x + \frac{1}{5}y = 87\times 10^4

    If you multiply both sides of the equation through by 5 then by 3 you will get

    5x + 3y = 1305\times 10^4

    and the system becomes...

    x + y = 290\times 10^4

    5x + 3y = 1305\times 10^4
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  3. #3
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    Thanks so much! It's perfectly clear now.
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