點計 Rate & Ratio ( F.2 數學 )

1)x:x+6 = 5:9
x / x+6 = 5 / 9
9x = 5x+30
x = 15/2

2) 2a+b = 6a-5b
6b = 4a
a/b = 6/4 = 3/2
i.e. a : b = 3 : 2

3a) 3a-4b=0
3a = 4b
a/b = 4/3
i.e. a:b=4:3
3b) 3a-4b = 0 ---(1)
a+b = 84 ..(2)
(1) - 3x(2) :
-4b - 3b = (-3)(84)
-7b = - 252
b = 36
so , a = 84-36 = 48

4a) let the days were sunny be x ,
so , The no. of rainy days was 3+x
As September has 30 days ,
x + (3+x) + 4 = 30
2x = 23 , x = 11.5 (check下題目有冇打錯 , day應該整數先岩)
4b) no. of rainy days / no. of sunny days.
= 3+11.5 / 11.5
= 29/23
so , the required ratio = 29 : 23

5) Let a' , b' represent the new values of a and b
a' = 1.2a , b' = 1.25b
a' / b' = 1.2a / 1.25b
= 0.96 (a/b )
= 0.96 (3/4) ( as a:b = 3:4)
= 0.72
= 18 / 25
so , the required ratio is 18 : 25

2009-09-12 10:47:51 補充：
第5 題應該 a'=1.2a , b'=0.75b
a' / b' = 1.2a / 0.75b
= 1.6 (a/b)
= 1.6(3/4)
= 1.2
= 6/5
so , the required ratio is 6:5

雖然我讀英中,識解,但我係f1