F.1 Mathz ,Ratio and Rate !!! 2 題 10分

1)
(i)
3a x 5 = 4k x 5
15a = 20k

(ii)
7b x 2 = 10k x 2
14b = 20k

(iii)
6c x 4 = 5k x 4
24c = 20k

(i) : (ii) : (iii) = a : b : c = 15 : 14 : 24

2)
(a)
0.5 : 1.5 : 3.0 = 4 : 9 : 7 = 4k : 9k : 7k

(b)
(4k x 0.5) + (9k x 1.5) + (7k x 3.0) = 73
2k + 13.5k + 21k = 73
36.5k = 73
k = 73 / 36.5
k = 2

the number of $0.5 stamps = 4k = 4 x 2 = 8
the number of $1.5 stamps = 9k = 9 x 2 = 18
the number of $3.0 stamps = 7k = 7 x 2 = 14

2007-04-14 15:12:16 補充：
3)Total distance between home and school 30 x 60 = 1,800mTime spent for the first 1,000m1,000 / 100 = 10 minsDistance of the remaining journey1,800 - 1,000 = 800mTime for the remaining journey30 - 10 = 20 minsSpeed for the remaining journey800 / 20 = 40m per min

2007-04-14 20:19:18 補充：
4)30 km/h : 10 m/s= 30 km/h : 0.010 km/s= 30 km/h : (0.010 x 60 x 60) km/h= 30 km/h : 36 km/h= 5 km/h : 6 km/h= 5 : 6

Question 1

3a = 4k
3a/4 = k

7b = 10k
7b/10 = k

6c = 5k
6c/5 = k

3a/4 = 7b/10 = 6c/5
15a = 14b = 24c
a:b:c = 15:14:24
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Question 2

(a)
Number of $1.5 stamps = 9k
Number of $3 stamps = 7k

(b)

4k(0.5) + 9k(1.5) + 7k (3) = 73
2k + 13.5k + 21k = 73
36.5k = 73
k = 2

Hence, the number of $0.5 stamps = 4 x 2 = 8 pieces
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Question 3

Total distance of the journey = 30 x 60 = 1800 m
Time spent for the initial 1000 m = 1000/100 = 10 mins
Walking speed for the remaining journey = (1800 - 1000)/20 = 800/20 = 40 m/min

1. first, find the LCM of 3, 7 and 6. LCM = 42
so we can write in the following way
3a * 14 = 4k * 14 ==> 42a = 56k
7b * 6 = 10k * 6 ==> 42b = 60k
6c * 7 = 5k * 7 ==> 42c = 35k
so 42a : 42b : 42c = a : b : c
where 42a : 42b : 42c = 56:60:35
so a:b : c = 56 : 60 : 35

2 (a) Let the numbers of $1.5 stamps and $ 3 stamps be a and b respectively
so we have 4:9:7 = 4k : a : b
the above equation can be divided into 2 parts
(1) (2)
4:9 = 4k : a 4:7 = 4k : b
4/9 = 4k / a 4/7 = 4k/b
a = 4k * 9 / 4 b = 4k * 7 /4
a=9k b=7k
So there are 9k $1.5 stamps and 7k $3 stamps

(b) from (a), 0.5 * 4k + 1.5 * 9k + 3 * 7k = 73
k = 2
So number of $0.5 stamps = 4*2 = 8

2007-04-14 15:14:53 補充：
3the total distance he has covered = 30 * 60 = 1800 mfor the first 1000m with 100m/min, he spends 1000/100 = 10 minsthe remaining distance = 1800 - 1000 = 800 mthe remaining time = 30 - 10 = 20 minso the speed for remaining journey = 800 / 20 = 40 m/min