Mrs Yong had a total of 104 white and purple lilies in the ratio of 10 : 3. After she had given away 5 times as many white lilies as purple lilies, the number of white and purple lilies left was in the ratio of 5 : 3. How many more white lilies than purple lilies did she give away?

	White	Purple	Total
Before	10 b	3 b	13 b
Change	- 5 u	- 1 u
After	5 p	3 p

	Make p the same (1)x3 = (3)	White (1)	Purple (2)	Make p the same (2)x5 = (4)
Before	240	80	24	120
Change	- 15 u	- 5 u	- 1 u	- 5 u
After	15 p	5 p	3 p	15 p

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

13 b = 104

1 b = 104 ÷ 13 = 8

Number of white lilies at first
= 10 b
= 10 x 8
= 80

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

80 - 5 u = 5 p --- (1)

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

Make p the same.

(1)_x3 
240 - 15 u = 15 p --- (3)

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

(3) = (4)
240 - 15 u = 120 - 5 u
15 u - 5 u = 240 - 120
10 u = 120

1 u = 120 ÷ 10 = 12

Number of more white lilies than purple lilies that she gave away
= 5 u - 1 u
= 4 u
= 4 x 12
= 48

Answer(s): 48