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Mere, Sam and Nathan go to a bookshop to buy supplies for their school. Mere bought two erasers and four pencils and paid $2.40 for it. Sam bought six erasers, one pencil and two pens and paid $3.95 while Nathan paid $4.15 for an eraser, a pencil and four pens. Write a system of equations that can be used to find the cost of each item.Use the inverse matrix method to solve the system of equations.
[Hint: use Gauss Jordan elimination]

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  1. If there are e erasers, p pencils, and q pens, we have

    2e+4p = 240
    6e+p+2q = 395
    e+p+4q = 415

    If A is the matrix of coefficients, then A^-1 =
    1/84
    (-2 16 -8)
    (22 -8 4)
    (-5 -2 22)

    Then you have
    (e p q) = (30 45 85)

    See here:

    http://www.wolframalpha.com/input/?i=inverse+%7B%7B2,4,0%7D,%7B6,1,2%7D,%7B1,1,4%7D%7D

    http://www.wolframalpha.com/input/?i=%7B%7B2,4,0%7D,%7B6,1,2%7D,%7B1,1,4%7D%7D*%7B%7Bx%7D,%7By%7D,%7Bz%7D%7D+%3D+%7B%7B240%7D,%7B395%7D,%7B415%7D%7D

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  2. cost of pencil --- p
    cost of eraser --- e
    cost of pen ----- x

    2e + 4p = 2.4 (1)
    6e + p + 2x = 3.95 (2)
    e + p + 4x = 4.15 (3)

    I would not use a matrix method, the equations are much too "nice".

    from (1) : e = 1.2 - 2p
    sub into (2)
    6(1.2 - 2p) + p + 2x = 3.95
    -11p + 2x = -3.25
    2x = 11p - 3.25
    4x = 22p - 6.5

    now sub those into (3)
    e + p + 4x = 4.15
    1.2 - 2p + p + 22p - 6.5 = 4.15
    21p = 9.45
    p = .45
    e = 1.2 - 2p = .30
    x = 13.60

    You can confirm my answer with this Gauss-Jordan applet
    http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

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  3. Looks like I messed up for my x
    I multiplied 4x by 4 instead of dividing by 4

    4x = 3.4
    x = .85

    see Steve's solution

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  4. DEAR SIR I NEED THE ANSWER OF THIS QUESTION PLEASE.Mere, Sam and Nathan go to a bookshop to buy supplies for their school. Mere bought
    two erasers and four pencils and paid $2.40 for it. Sam bought six erasers, one pencil and
    two pens and paid $3.95 while Nathan paid $4.15 for an eraser, a pencil and four pens.
    a) Write a system of equations that can be used to find the cost of each item.
    b) Use an appropriate method to solve the system of equations

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