Help me Mathematics from F2

Three positive numbers are in the ratio 3:4:5.If the difference between the larest number and the smallest number is 10.find the number.


Let 3k, 4k and 5k be the three positive numbers.

5k - 3k = 10
2k = 10
k = 5

3k = 15
4k = 20
5k = 25

The three numbers are 15, 20 and 25.

a/b = 5/4...(1)

b/c = 4/3...(2)

a/c = 5/3...(3)



a-c = 10

a = 10+c...(4)



sub (4) into (3)

10+c / c = 5/3

30+3c = 5c

2c = 30

c = 15...(5)



Sub (5) into (3)

a/c = 5/3

a/15 = 5/3

3a = 75

a = 25... (6)



Sub (6) into (1)

a/b= 5/4

25/b=5/4

5b = 100

b = 20



c:b:a = 3:4:5

15:20:25 = 3:4:5

1/5 (3:4:5) = 3:4:5 (OK)



SO the three number is
15:20:25

2010-06-18 22:03:21 補充：
Another simple method
3:4:5
3x+10 = 5x
2x = 10
x = 5
(means.... One portion is 5)

first number has 3 portion = 15
second number has 4 portion = 20
third portion has 5 portion = 25