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Math Help - Find Combined Cost

  1. #1
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    Find Combined Cost

    Three shirts and 2 neckties cost $69. At the same prices, 2 shirts and 3 neckties cost $61. What is the combined cost of one shirt and one necktie?

    I realize this is a system of linear equations in 2 variables.

    Let s = shirts and n = neckties

    I came up with the following two equations:

    3s + 2n = 69
    2s + 3n = 61

    Is this right so far?

    I came up with a combined cost of $35.

    The right answer is $26. What did I do wrong?
    How do I get $26?
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  2. #2
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    Hallo mangentarita!

    Quote Originally Posted by magentarita View Post
    Three shirts and 2 neckties cost $69. At the same prices, 2 shirts and 3 neckties cost $61. What is the combined cost of one shirt and one necktie?

    I realize this is a system of linear equations in 2 variables.
    Okay.

    Quote Originally Posted by magentarita View Post
    Let s = shirts and n = neckties
    Well, s = price of one shirt and n = price of one necktie.


    Quote Originally Posted by magentarita View Post
    I came up with the following two equations:

    3s + 2n = 69
    2s + 3n = 61

    Is this right so far?
    Yes, it is.

    Quote Originally Posted by magentarita View Post
    I came up with a combined cost of $35.

    The right answer is $26. What did I do wrong?
    I don't know. Misscalculation?

    The equations
    3s + 2n = 69
    2s + 3n = 61

    are solved by n=$9 and s = $17

    Quote Originally Posted by magentarita View Post
    How do I get $26?
    9+17 = 26

    You failed in solving the two equations

    Try again?

    Regards, Rapha
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  3. #3
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    Hello, magentarita!

    Three shirts and 2 neckties cost $69.
    At the same prices, 2 shirts and 3 neckties cost $61.
    What is the combined cost of one shirt and one necktie?

    I realize this is a system of linear equations in 2 variables.

    Let s = shirts and n = neckties

    I came up with the following two equations: . \begin{array}{ccc}3s + 2n &=& 69 \\ 2s + 3n &=& 61 \end{array}

    Is this right so far? . Yes, good work!
    It's hard to see your work from here,
    . . but it looks you played the 8\heartsuit instead of the K\spadesuit.

    But seriously, there is a back-door solution to this problem.


    Add the two equations: . 5s + 5n \:=\:130

    . . Therefore: . \boxed{s + n \:=\:26}

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  4. #4
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    ok...

    Quote Originally Posted by Rapha View Post
    Hallo mangentarita!



    Okay.



    Well, s = price of one shirt and n = price of one necktie.




    Yes, it is.



    I don't know. Misscalculation?

    The equations
    3s + 2n = 69
    2s + 3n = 61

    are solved by n=$9 and s = $17



    9+17 = 26

    You failed in solving the two equations

    Try again?

    Regards, Rapha
    I thank you. I got the wrong answer for n. I somehow got n = 18.
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  5. #5
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    ok...

    Quote Originally Posted by Soroban View Post
    Hello, magentarita!

    It's hard to see your work from here,
    . . but it looks you played the 8\heartsuit instead of the K\spadesuit.

    But seriously, there is a back-door solution to this problem.


    Add the two equations: . 5s + 5n \:=\:130

    . . Therefore: . \boxed{s + n \:=\:26}
    I miss your replies. Thank you. How have you been?
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