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basic math

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An education fund allocates RM10,000 to help 100 students from form three, form five and form six in a school. Each form three student receives RM80, each form five student receives RM120 and each form six student receives RM160. The number of form three students that receive the aid is twice the number of form five students.
(a) Form a system of linear equations from the above information.
(b) Hence, determine the number of students for each form that receive the aid by using matrices.

  • basic math -

    Form three students --- x
    form five students ---- y
    form six students ----- 100-x-y

    80x + 120y + 160(100-x-y) = 10000
    80x + 120y + 16000-160x-160y = 10000
    -80x - 40y = -6000
    2x + y = 150

    but it said:
    x = 2y
    2(2y) + y = 150
    y = 30
    x = 2y = 60
    remaining students = 100-30-60 = 10

    I did not use matrices on such a simple problem because solving it was so much easier using the above method,
    but.... if you have to use matrices

    our two equations are:
    2x + y = 150
    x - 2y = 0

    2 1 150
    1 -2 0 ---->

    4 2 300
    1 -2 0 --->

    1 -2 0
    4 2 300 ---> add

    1 -2 0
    5 0 300

    1 -2 0
    1 0 60

    from the last x=60
    in 1st: 60-2y=0
    -2y=-60
    y=30
    etc

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