Mrs Chia had a total of 144 purple and white roses in the ratio of 7 : 2. After she had given away 6 times as many purple roses as white roses, the number of purple and white roses left was in the ratio of 8 : 3. How many more purple roses than white roses did she give away?

	Purple	White	Total
Before	7 b	2 b	9 b
Change	- 6 u	- 1 u
After	8 p	3 p

	Make p the same (1)x3 = (3)	Purple (1)	White (2)	Make p the same (2)x8 = (4)
Before	336	112	32	256
Change	- 18 u	- 6 u	- 1 u	- 8 u
After	24 p	8 p	3 p	24 p

Number of roses at first
= 7 b + 2 b
= 9 b

9 b = 144

1 b = 144 ÷ 9 = 16

Number of purple roses at first
= 7 b
= 7 x 16
= 112

Number of white roses at first
= 2 b
= 2 x 16
= 32

112 - 6 u = 8 p --- (1)

32 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
336 - 18 u = 24 p --- (3)

(2)_x8 = (4)
256 - 8 u = 24 p --- (4)

(3) = (4)
336 - 18 u = 256 - 8 u
18 u - 8 u = 336 - 256
10 u = 80

1 u = 80 ÷ 10 = 8

Number of more purple roses than white roses that she gave away
= 6 u - 1 u
= 5 u
= 5 x 8
= 40

Answer(s): 40