Mrs Goh had a total of 52 yellow and pink lilies in the ratio of 10 : 3. After she had given away 4 times as many yellow lilies as pink lilies, the number of yellow and pink lilies left was in the ratio of 4 : 3. How many more yellow lilies than pink lilies did she give away?

	Yellow	Pink	Total
Before	10 b	3 b	13 b
Change	- 4 u	- 1 u
After	4 p	3 p

	Make p the same (1)x3 = (3)	Yellow (1)	Pink (2)	Make p the same (2)x4 = (4)
Before	120	40	12	48
Change	- 12 u	- 4 u	- 1 u	- 4 u
After	12 p	4 p	3 p	12 p

Number of lilies at first
= 10 b + 3 b
= 13 b

13 b = 52

1 b = 52 ÷ 13 = 4

Number of yellow lilies at first
= 10 b
= 10 x 4
= 40

Number of pink lilies at first
= 3 b
= 3 x 4
= 12

40 - 4 u = 4 p --- (1)

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

Make p the same.

(1)_x3 
120 - 12 u = 12 p --- (3)

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

(3) = (4)
120 - 12 u = 48 - 4 u
12 u - 4 u = 120 - 48
8 u = 72

1 u = 72 ÷ 8 = 9

Number of more yellow lilies than pink lilies that she gave away
= 4 u - 1 u
= 3 u
= 3 x 9
= 27

Answer(s): 27