Mrs Lin had a total of 98 white and yellow roses in the ratio of 9 : 5. After she had given away 3 times as many white roses as yellow roses, the number of white and yellow roses left was in the ratio of 3 : 2. How many more white roses than yellow roses did she give away?

	White	Yellow	Total
Before	9 b	5 b	14 b
Change	- 3 u	- 1 u
After	3 p	2 p

	Make p the same (1)x2 = (3)	White (1)	Yellow (2)	Make p the same (2)x3 = (4)
Before	126	63	35	105
Change	- 6 u	- 3 u	- 1 u	- 3 u
After	6 p	3 p	2 p	6 p

Number of roses at first
= 9 b + 5 b
= 14 b

14 b = 98

1 b = 98 ÷ 14 = 7

Number of white roses at first
= 9 b
= 9 x 7
= 63

Number of yellow roses at first
= 5 b
= 5 x 7
= 35

63 - 3 u = 3 p --- (1)

35 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
126 - 6 u = 6 p --- (3)

(2)_x3 = (4)
105 - 3 u = 6 p --- (4)

(3) = (4)
126 - 6 u = 105 - 3 u
6 u - 3 u = 126 - 105
3 u = 21

1 u = 21 ÷ 3 = 7

Number of more white roses than yellow roses that she gave away
= 3 u - 1 u
= 2 u
= 2 x 7
= 14

Answer(s): 14