Mrs Oh had a total of 66 white and purple roses in the ratio of 9 : 2. After she had given away 5 times as many white roses as purple roses, the number of white and purple roses left was in the ratio of 7 : 2. How many more white roses than purple roses did she give away?

	White	Purple	Total
Before	9 b	2 b	11 b
Change	- 5 u	- 1 u
After	7 p	2 p

	Make p the same (1)x2 = (3)	White (1)	Purple (2)	Make p the same (2)x7 = (4)
Before	108	54	12	84
Change	- 10 u	- 5 u	- 1 u	- 7 u
After	14 p	7 p	2 p	14 p

Number of roses at first
= 9 b + 2 b
= 11 b

11 b = 66

1 b = 66 ÷ 11 = 6

Number of white roses at first
= 9 b
= 9 x 6
= 54

Number of purple roses at first
= 2 b
= 2 x 6
= 12

54 - 5 u = 7 p --- (1)

12 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
108 - 10 u = 14 p --- (3)

(2)_x7 = (4)
84 - 7 u = 14 p --- (4)

(3) = (4)
108 - 10 u = 84 - 7 u
10 u - 7 u = 108 - 84
3 u = 24

1 u = 24 ÷ 3 = 8

Number of more white roses than purple roses that she gave away
= 5 u - 1 u
= 4 u
= 4 x 8
= 32

Answer(s): 32