Mrs Yong had a total of 198 purple and white roses in the ratio of 8 : 3. After she had given away 4 times as many purple roses as white roses, the number of purple and white roses left was in the ratio of 5 : 2. How many more purple roses than white roses did she give away?

	Purple	White	Total
Before	8 b	3 b	11 b
Change	- 4 u	- 1 u
After	5 p	2 p

	Make p the same (1)x2 = (3)	Purple (1)	White (2)	Make p the same (2)x5 = (4)
Before	288	144	54	270
Change	- 8 u	- 4 u	- 1 u	- 5 u
After	10 p	5 p	2 p	10 p

Number of roses at first
= 8 b + 3 b
= 11 b

11 b = 198

1 b = 198 ÷ 11 = 18

Number of purple roses at first
= 8 b
= 8 x 18
= 144

Number of white roses at first
= 3 b
= 3 x 18
= 54

144 - 4 u = 5 p --- (1)

54 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
288 - 8 u = 10 p --- (3)

(2)_x5 = (4)
270 - 5 u = 10 p --- (4)

(3) = (4)
288 - 8 u = 270 - 5 u
8 u - 5 u = 288 - 270
3 u = 18

1 u = 18 ÷ 3 = 6

Number of more purple roses than white roses that she gave away
= 4 u - 1 u
= 3 u
= 3 x 6
= 18

Answer(s): 18