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Mario 發問於 科學及數學數學 · 6 年前

S2 maths rate and ratio,help!!

please show the steps

simplify the following ratio

1a) 3:9:15

1b) 3:1/3:1/9

find x:y:z in each of the following

2a)x:y=3:4,y:z=5:6

2b)x:y=2:3,x:z=5:1

2c)y:z=3:4,x:z=1:6

2d)x:y=y:z=3:5

3)In a mathematics competition, Simon, Jill and Hugo source 66 ,54 and 78 marks respectively. Find the ratio of their scores.

4)ABCD is a line segment. The lengths of AB,BC and CD are 6 cm , 8 cm and 12 cm respectively.Find the following ratios .

5)A sum of $640 is to be shared by three person three persons A , B and C in the ratio 7 : 4 : 5 .How much will each person get ?

6)The heights of Wilson and Sam are in the ratio 8 : 9 .If Wilson's height is 160 cm , how tall is Sam ?

7)Mr Fei and Mr Tai weight 156 kg and 117 kg respectively. They are going to share a bottle of coke in the ratio of their weights. If Mr Tai gets 450 mL of coke , what is the total volume of the bottle of coke in litres?

simplify the following ratios

8a) 8/9 :1.6

8b)2.1: 2+1/3

8c)275cm² : 1/4 m²

8d)1 hour and 4 minutes : 2 hours and 40 minutes

find the unknown in the followun

9a) (x+2):x =3:2

9b)y:5 =(y-6):3

The hw need to hand in before 3/10 ,please help me before 3/10

2 個解答

評分
  • 土扁
    Lv 7
    6 年前
    最愛解答

    1)

    a)

    3 : 9 : 15

    = 3/3 : 9/3 : 15/3

    = 1 :3 : 5

    b)

    3 : 1/3 : 1/9

    = 3×9 : (1/3)×9: (1/9)×9

    = 27 : 3 : 1

    ====

    2)

    a)

    x : y = 3 : 4 =15 : 20

    y : z = 5 : 6 =20 : 24

    x : y : z = 15 : 20 : 24

    b)

    x : y = 2 : 3 =10 : 15

    x : z = 5 : 1 =10 : 2

    x : y : z = 10 : 15 : 2

    c)

    y : z = 3 : 4 =9 : 12

    x : z = 1 : 6 =2 : 12

    x : y : z = 2 : 9 : 12

    d)

    x : y =3 : 5 = 9 : 15

    y : z = 3 : 5 =15 : 25

    x : y : z = 9 : 15 : 25

    ====

    3)

    Simon's score : Jill's score : Hugo's score

    = 66 : 54 : 78

    = 66/6 : 54/6 : 78/6

    = 11 : 9 : 13

    ====

    4)

    AB : BC : CD

    = 6 : 8 : 12

    = 3 : 4 : 6

    However, what do you mean by "the following ratios" ?

    ====

    5)

    A gets = $640 × [7/(7 + 4 + 5)] = $280

    B gets = $640 × [4/(7 + 4 + 5)] = $160

    C gets = $640 × [5/(7 + 4 + 5)] = $200

    ====

    6)

    Sam's height

    = 160 × (9/8) cm

    = 180 cm

    ====

    7)

    Total volume of coke

    = 450 × [(156 + 117)/117] mL

    = 1050 mL

    ====

    8)

    a)

    8/9 : 1.6

    = (8/9)×(9/8) : 1.6×(9/8)

    = 1 : 1.8

    = 10/2 : 18/2

    = 5 : 9

    b)

    2.1 : (2+1/3)

    = 2.1 : (7/3)

    = 2.1×(3/7) : (7/3)×(3/7)

    = 0.9 : 1

    = 9 : 10

    c)

    275 cm² : 1/4 m²

    = 275 cm² : (1/4)×100² m²

    = 275 : 2500

    = 275/25 : 2500/25

    = 11 : 100

    d)

    1 h and 4 min : 2 h and 40 min

    = (60 + 4) min : (2×60 + 40) min

    = 64 : 160

    = 64/32 : 160/32

    = 2 : 5

    ====

    9

    a)

    (x + 2) : x = 3 : 2

    3x = 2(x + 2)

    3x = 2x + 4

    x = 4

    b)

    y : 5 = (y - 6) : 3

    5(y - 6) = 3y

    5y - 30 = 3y

    2y = 30

    y = 15

    資料來源: 土扁
    • Commenter avatar登入以回覆解答
  • 1a)

    3:9:15

    = 3:3x3:3x5

    = 1:3:5 ... ( both * 1/3)

    1b)

    3:1/3:1/9

    = 3*9:1/3*9:1/9*9

    = 27:3:1 ... ( both * 9)

    9a)

    (x+2):x =3:2

    (x+2)/x = 3/2

    2(x+2) = 3x

    2*2 = 3x - 2x

    x = 4

    9b)

    y:5 =(y-6):3

    y/5 = (y-6)/3

    3y = 5(y-6)

    5y - 3y = -5*6

    2y = 30

    y = 15

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