急急急急急!中一率及比問題(要步驟,15點)

[1]如果4x-5y=0;求(3x-y):(2x+3y).
4x = 5y
x = (5/4) y
(3(5/4) y -y) : (2 (5/4)y +3y).
(15/4y – y) : 5.5y
(11/4) y: 11/2 y
11y : 22 y
1: 2
(3x-y):(2x+3y) 1:2

[2]如果a:b=2:3及b:c=4:5,求(3a-b):(b+2c)
a/b = 2/3, so a = (2/3)b
b/c = 4/5, so c = (5/4) b
(3a-b):(b+2c) (3(2/3)b -b): (b+2(5/4) b)
(2b -b): (b+2.5 b)
b : 3.5b = 2b: 7b
2:7
(3a-b):(b+2c) 2:7

[3]如果2x= 3y = 4z, 求(x-y+z):(x+y-z).
x = 1.5y, z = 0.75y
(x-y+z):(x+y-z)
(1.5y – y + 0.75y) : (1.5y +y – 0.75y)
1.25y : 1.75y
125:175
5 : 7
(x-y+z):(x+y-z). 5: 7

[4]如果a:b=3:5及b:c=3:2,求2a+3b-c÷3a-2b+c.
a/b = 3/5, so a = (3/5) b
b/c = 3/2, so c =(2/3) b
2a+3b-c = 2(3/5)b + 3b – (2/3)b = 1.2 b + 3b – (2/3) b = (21/5)b – (2/3)b = (53/15)b
3a-2b+c = 3(3/5)b - 2b + (2/3)b (7/15) b
2a+3b-c. (53/15) b 53
------------- = ----------------- = ----
3a-2b+c. (7/15) b 7

2a+3b-c÷3a-2b+c. = 53/7

[5]某地圖的比例尺是1:120000;如果一條公路的實際長度是3km,求該條公路在地圖上的長度(答案以cm為單位.)
3 km/120000 = 300000 cm/120000 = 2.5 cm
該條公路在地圖上的長度 = 2.5 cm

[6]如果(3a+2b):(a+6b)=2:1;求
(a)a:b;
(3a + 2b)/(a + 6b) = 2/1
3a + 2b = 2(a + 6b)
3a + 2b = 2a + 12b
a = 12b
a/b = 12/1
a:b 12: 1

(b) (2a+b):(3a-b)
2(12b) +b : 3(12b) –b
24b + b : 36b – b
25b :35b
5: 7
(2a+b):(3a-b) 5: 7