Mrs Chan had a total of 143 yellow and purple roses in the ratio of 7 : 4. After she had given away 3 times as many yellow roses as purple roses, the number of yellow and purple roses left was in the ratio of 4 : 3. How many more yellow roses than purple roses did she give away?

	Yellow	Purple	Total
Before	7 b	4 b	11 b
Change	- 3 u	- 1 u
After	4 p	3 p

	Make p the same (1)x3 = (3)	Yellow (1)	Purple (2)	Make p the same (2)x4 = (4)
Before	273	91	52	208
Change	- 9 u	- 3 u	- 1 u	- 4 u
After	12 p	4 p	3 p	12 p

Number of roses at first
= 7 b + 4 b
= 11 b

11 b = 143

1 b = 143 ÷ 11 = 13

Number of yellow roses at first
= 7 b
= 7 x 13
= 91

Number of purple roses at first
= 4 b
= 4 x 13
= 52

91 - 3 u = 4 p --- (1)

52 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
273 - 9 u = 12 p --- (3)

(2)_x4 = (4)
208 - 4 u = 12 p --- (4)

(3) = (4)
273 - 9 u = 208 - 4 u
9 u - 4 u = 273 - 208
5 u = 65

1 u = 65 ÷ 5 = 13

Number of more yellow roses than purple roses that she gave away
= 3 u - 1 u
= 2 u
= 2 x 13
= 26

Answer(s): 26