Mrs Ong had a total of 104 purple and white tulips in the ratio of 9 : 4. After she had given away 4 times as many purple tulips as white tulips, the number of purple and white tulips left was in the ratio of 5 : 3. How many more purple tulips than white tulips did she give away?

	Purple	White	Total
Before	9 b	4 b	13 b
Change	- 4 u	- 1 u
After	5 p	3 p

	Make p the same (1)x3 = (3)	Purple (1)	White (2)	Make p the same (2)x5 = (4)
Before	216	72	32	160
Change	- 12 u	- 4 u	- 1 u	- 5 u
After	15 p	5 p	3 p	15 p

Number of tulips at first
= 9 b + 4 b
= 13 b

13 b = 104

1 b = 104 ÷ 13 = 8

Number of purple tulips at first
= 9 b
= 9 x 8
= 72

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

72 - 4 u = 5 p --- (1)

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

Make p the same.

(1)_x3 
216 - 12 u = 15 p --- (3)

(2)_x5 = (4)
160 - 5 u = 15 p --- (4)

(3) = (4)
216 - 12 u = 160 - 5 u
12 u - 5 u = 216 - 160
7 u = 56

1 u = 56 ÷ 7 = 8

Number of more purple tulips than white tulips that she gave away
= 4 u - 1 u
= 3 u
= 3 x 8
= 24

Answer(s): 24