Mrs Lin had a total of 104 pink and yellow lilies in the ratio of 9 : 4. After she had given away 4 times as many pink lilies as yellow lilies, the number of pink and yellow lilies left was in the ratio of 4 : 3. How many more pink lilies than yellow lilies did she give away?

	Pink	Yellow	Total
Before	9 b	4 b	13 b
Change	- 4 u	- 1 u
After	4 p	3 p

	Make p the same (1)x3 = (3)	Pink (1)	Yellow (2)	Make p the same (2)x4 = (4)
Before	216	72	32	128
Change	- 12 u	- 4 u	- 1 u	- 4 u
After	12 p	4 p	3 p	12 p

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

13 b = 104

1 b = 104 ÷ 13 = 8

Number of pink lilies at first
= 9 b
= 9 x 8
= 72

Number of yellow lilies at first
= 4 b
= 4 x 8
= 32

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

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

Make p the same.

(1)_x3 
216 - 12 u = 12 p --- (3)

(2)_x4 = (4)
128 - 4 u = 12 p --- (4)

(3) = (4)
216 - 12 u = 128 - 4 u
12 u - 4 u = 216 - 128
8 u = 88

1 u = 88 ÷ 8 = 11

Number of more pink lilies than yellow lilies that she gave away
= 4 u - 1 u
= 3 u
= 3 x 11
= 33

Answer(s): 33