Mrs Yong had a total of 44 white and purple tulips in the ratio of 8 : 3. After she had given away 4 times as many white tulips as purple tulips, the number of white and purple tulips left was in the ratio of 4 : 3. How many more white tulips than purple tulips did she give away?

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

	Make p the same (1)x3 = (3)	White (1)	Purple (2)	Make p the same (2)x4 = (4)
Before	96	32	12	48
Change	- 12 u	- 4 u	- 1 u	- 4 u
After	12 p	4 p	3 p	12 p

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

11 b = 44

1 b = 44 ÷ 11 = 4

Number of white tulips at first
= 8 b
= 8 x 4
= 32

Number of purple tulips at first
= 3 b
= 3 x 4
= 12

32 - 4 u = 4 p --- (1)

12 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
96 - 12 u = 12 p --- (3)

(2)_x4 = (4)
48 - 4 u = 12 p --- (4)

(3) = (4)
96 - 12 u = 48 - 4 u
12 u - 4 u = 96 - 48
8 u = 48

1 u = 48 ÷ 8 = 6

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

Answer(s): 18