Mario 發問於 科學及數學數學 · 6 年前

# S2 maths rate and ratio,help!!

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

### 2 個解答

• 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
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• 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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