Mrs Tang had a total of 132 yellow and purple daisies in the ratio of 7 : 4. After she had given away 3 times as many yellow daisies as purple daisies, the number of yellow and purple daisies left was in the ratio of 3 : 2. How many more yellow daisies than purple daisies did she give away?

	Yellow	Purple	Total
Before	7 b	4 b	11 b
Change	- 3 u	- 1 u
After	3 p	2 p

	Make p the same (1)x2 = (3)	Yellow (1)	Purple (2)	Make p the same (2)x3 = (4)
Before	168	84	48	144
Change	- 6 u	- 3 u	- 1 u	- 3 u
After	6 p	3 p	2 p	6 p

Number of daisies at first
= 7 b + 4 b
= 11 b

11 b = 132

1 b = 132 ÷ 11 = 12

Number of yellow daisies at first
= 7 b
= 7 x 12
= 84

Number of purple daisies at first
= 4 b
= 4 x 12
= 48

84 - 3 u = 3 p --- (1)

48 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
168 - 6 u = 6 p --- (3)

(2)_x3 = (4)
144 - 3 u = 6 p --- (4)

(3) = (4)
168 - 6 u = 144 - 3 u
6 u - 3 u = 168 - 144
3 u = 24

1 u = 24 ÷ 3 = 8

Number of more yellow daisies than purple daisies that she gave away
= 3 u - 1 u
= 2 u
= 2 x 8
= 16

Answer(s): 16