Mrs Zhang had a total of 80 pink and purple lilies in the ratio of 7 : 3. After she had given away 3 times as many pink lilies as purple lilies, the number of pink and purple lilies left was in the ratio of 5 : 3. How many more pink lilies than purple lilies did she give away?

	Pink	Purple	Total
Before	7 b	3 b	10 b
Change	- 3 u	- 1 u
After	5 p	3 p

	Make p the same (1)x3 = (3)	Pink (1)	Purple (2)	Make p the same (2)x5 = (4)
Before	168	56	24	120
Change	- 9 u	- 3 u	- 1 u	- 5 u
After	15 p	5 p	3 p	15 p

Number of lilies at first
= 7 b + 3 b
= 10 b

10 b = 80

1 b = 80 ÷ 10 = 8

Number of pink lilies at first
= 7 b
= 7 x 8
= 56

Number of purple lilies at first
= 3 b
= 3 x 8
= 24

56 - 3 u = 5 p --- (1)

24 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
168 - 9 u = 15 p --- (3)

(2)_x5 = (4)
120 - 5 u = 15 p --- (4)

(3) = (4)
168 - 9 u = 120 - 5 u
9 u - 5 u = 168 - 120
4 u = 48

1 u = 48 ÷ 4 = 12

Number of more pink lilies than purple lilies that she gave away
= 3 u - 1 u
= 2 u
= 2 x 12
= 24

Answer(s): 24