F.1數學 20點急急急急急要的!!

F.1數學 20點急急急急急要的!!

12) Find x : y : z for each of the following .
12a) x : y = 2 : 1 , y : z = 1: 10

A. x:y = 2:1
y:z = 1:10
x:y:z = 2*1 : 1*1 : 1*10
x:y:z = 2:1:10

12b) x : y = 1 : 2 , y : z = 2 : 5

A. x:y = 1:2
y:z = 2:5
x:y:z = 1*2 : 2*2 : 2*5
x:y:z = 2:4:10
x:y:z = 1:2:5

12c) x : y = 9 : 4 , y : z = 4 : 3

A. x:y = 9:4
y:z = 4:3
x:y:z = 9*4 : 4*4 : 3*4
x:y:z = 36:16:12
x:y:z = 9:4:3

14a) a / b = 1 , b / c = 1 / 2

A. a/b = 1
a:b = 1:1

b/c = 1/2
b:c = 1:2

a:b:c = 1*1 : 1*1 : 2*2
a:b:c = 1:1:2

14b) a / b = 1 / 2 , b = 3c

A. a/b = 1/2
a:b = 1:2

b = 3c
b/c = 3/1
b:c = 3:1

a:b:c = 1*3 : 2*3 : 2*1
a:b:c = 3:6:2

14c) 4a = 5b = 2c

A. 4a = 5b
a/b = 5/4
a:b = 5:4

5b = 2c
b/c = 2/5
b:c = 2:5

a:b:c = 5*2 : 4*2 : 4*5
a:b:c = 10:8:20
a:b:c = 5:4:10

15) There are 45 gold coins , 60 silver coins and 90 copper coins in a bag . Find the ratio of the number of gold coins , silver coins and copper coins in the bag .

A. the ratio of the number of gold coins , silver coins and copper coins in the bag
= 45:60:90
= 45/15 : 60/15 : 90/15
= 3:4:6

16) Cindy has 6 English books , 10 Chinese books and 2 Japanese books .
16a) Find the ratio of the number of English books , Chinese books and Japanese books .

A. the ratio of the number of English books , Chinese books and Japanese books
= 6:10:2
= 6/2 : 10/2 : 2/2
= 3:5:1

16b) If Cindy buys 2 English books , 2 Chinese books and 4 Japanese books , find the ratio of the number of English books , Chinese books and Japanese books owned by Cindy now .

A. the ratio of the number of English books , Chinese books and Japanese books owned by Cindy now
= (6+2):(10+2):(2+4)
= 8:12:6
= 8/2 : 12/2 : 6/2
= 4:6:3

2010-05-09 19:30:53 補充：
To 003:

There is a quicker method for 16a) and 16b).

12a) x : y = 2 : 1 , y : z = 1: 10
x:y =2:1
y:z= 1:10
x:y:z=2:1:10

12b) x : y = 1 : 2 , y : z = 2 : 5
x:y =1:2
y:z= 2:5
x:y:x=1:2:5

12c) x : y = 9 : 4 , y : z = 4 : 3
x:y =9:4
y:z = 4:3
x:y:z =9:4:3

14a) a / b = 1 , b / c = 1 / 2
a:b =1:1
b:c = 1:2
a:b:c = 1:1:2

14b) a / b = 1 / 2 , b = 3c
b/c=3
a:b =1:2
b:c= 3:1
a:b:c=3:6:2

14c) 4a = 5b = 2c
a/b=5/4
b/c=2/5
a:b =5:4
b:c= 2:5
a:b:c=5:4:10

15)The ratio.
=45 :60 : 90
= 7 :12 : 18

16a)The ratio.
=6:10:2
=3: 5 :1
16b)The ratio.
=8:12:6
=4:6 :3

12)
a)
x : y : =2 : 1
y : z = 1 : 10
x : y : z =2 : 1 : 10
b)
x : y : =1 : 2
y : z = 2 : 5
x : y : z =1 : 2 : 5
c)
x : y : =9 : 4
y : z = 4 : 3
x : y : z =9 : 4 : 3

14)
a)
a/b=1,a:b=1:1
b/c=1/2,b:c=1:2
a : b : =1 : 1
b : c = 1 : 2
a : b : c =1 : 1 : 2
b)
a/b=1/2,a:b=1:2
b=3c,b/c=3,b:c=3:1
a : b : =1 : 2
b : c = 3 :1
a : b : c =3 : 6 : 2
c)4a=5b=2c
1: 4a=5b,a/b=5/4,a:b=5:4
2: 5b=2c,b/c=2/5,b:c=2:5
a : b : =5 : 4
b : c = 2 : 5
a : b : c =5 : 4 : 10

15)Let 45x(gold coins),60y(silver coins),90z(copper coins)
1: x:y=45:60
= 3:4
2: y:z=60:90
= 2:3
x : y : =3 :4
y : z = 2 : 3
x : y : z =3 : 4 : 6

16)Let 6x(English books),10y(Chinese books),2z(Japanese books)
a)
1:x:y=6:10
=3:5
2:y:z=10:2
= 5:1
x : y : =3 : 5
y : z = 5 : 1
x : y : z =3 : 5 : 1
b)Let 8x(English books),12y(Chinese books),6z(Japanese books)
1:x:y=8:12
=2:3
2:y:z=12:6
= 2:1
x : y : =2 : 3
y : z = 2 : 1
x : y : z =4 : 6 : 3

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