Mrs Lin had a total of 260 purple and yellow lilies in the ratio of 10 : 3. After she had given away 6 times as many purple lilies as yellow lilies, the number of purple and yellow lilies left was in the ratio of 8 : 3. How many more purple lilies than yellow lilies did she give away?

	Purple	Yellow	Total
Before	10 b	3 b	13 b
Change	- 6 u	- 1 u
After	8 p	3 p

	Make p the same (1)x3 = (3)	Purple (1)	Yellow (2)	Make p the same (2)x8 = (4)
Before	600	200	60	480
Change	- 18 u	- 6 u	- 1 u	- 8 u
After	24 p	8 p	3 p	24 p

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

13 b = 260

1 b = 260 ÷ 13 = 20

Number of purple lilies at first
= 10 b
= 10 x 20
= 200

Number of yellow lilies at first
= 3 b
= 3 x 20
= 60

200 - 6 u = 8 p --- (1)

60 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
600 - 18 u = 24 p --- (3)

(2)_x8 = (4)
480 - 8 u = 24 p --- (4)

(3) = (4)
600 - 18 u = 480 - 8 u
18 u - 8 u = 600 - 480
10 u = 120

1 u = 120 ÷ 10 = 12

Number of more purple lilies than yellow lilies that she gave away
= 6 u - 1 u
= 5 u
= 5 x 12
= 60

Answer(s): 60