sui lin 發問於 科學及數學數學 · 1 十年 前

about maths(HElp)

The chapter is about (Simultaneous Linear Equations in Two Unknows)

I Have 2 questions to ask.

1. x+9/3 - y-10/2= x+5y/2=4

2.There are two sections in a Mathematics test.Each correct answer in Section A scores 2 marks, while each in section B scores 3 marks.If Johnny has answerd 40 questions correctly and scored 92 marks, find the number of questions he has answerd correctly in Section A and B respectively.

**THX

2 個解答

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    1 十年 前
    最佳解答

    1.

    x+9/3 - y-10/2= x+5y/2=4

    (x + 5y)/2 = 4

    x + 5y = 8

    x = 8 - 5y---------------(1)

    x+9/3 - y-10/2 = 4

    2(x + 9) - 3(y + 10) = 24

    2x + 18 - 3y - 30 = 24

    2x - 3y = 36----------------(2)

    sub (1) into (2)

    2(8 - 5y) - 3y = 36

    16 - 10y - 3y = 36

    -13y = 20

    y = - 20/13

    sub y = -20/13 into (1)

    x = 8 - 5( - 20/13)

    13x = 104 + 100

    13x = 204

    x = 204/13

    so, x = 204/13,y = - 20/13

    2).There are two sections in a Mathematics test.Each correct answer in Section A

    scores 2 marks, while each in section B scores 3 marks.If Johnny has answerd 40

    questions correctly and scored 92 marks, find the number of questions he has

    answered

    correctly in Section A and B respectively.

    Let x and y be the number of question that he has answered correctly in Section A and

    B respectively,

    2x + 3y = 92----------------(1)

    x + y = 40----------------(2)

    (2) x 2:

    2x +2y = 80

    (1) - (2):

    y = 12

    sub y = 12 into (2)

    x = 28

    so,he has answerd correctly 28 questions in Section A and 12 questions in Section B

    respectively.

    資料來源: by eason mensa
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  • 1 十年 前

    1.the simultaneous equations can be rewritten as:(跟足Format)

    {x+9/3 - y-10/2=4_____(1)

    {x+5y/2=4________(2)

    From (2), we get that x=4-5y/2______(3)

    Substitute (3) into (1),

    (4-5y/2+9)/3 - (y-10)/2=4

    (8-5y+18+3y+30)/6=4

    56-2y=6x4

    56-24=2y

    y=16.

    Substitute y=16 into (3),

    x=4-5(16)/2

    =-38

    So the solution is x=-38, y=16.(唔知啱唔啱)

    2.Let x be the number of questions in Section A that Johnny has answered correctly, then the number of questions in Section B that Johnny has answered correctly is 40-x.

    2x+3(40-x)=92

    2x+120-3x=92

    120-92=3x-2x

    so x=28.

    The number of questions in Section A that Johnny has answered correctly is 28,and the number of questions in Section B that Johnny has answered correctly is 40-28=12 questions.(唔知啱唔啱)

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