Mrs Lin had a total of 209 purple and yellow lilies in the ratio of 7 : 4. 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 5 : 4. How many more purple lilies than yellow lilies did she give away?

	Purple	Yellow	Total
Before	7 b	4 b	11 b
Change	- 6 u	- 1 u
After	5 p	4 p

	Make p the same (1)x4 = (3)	Purple (1)	Yellow (2)	Make p the same (2)x5 = (4)
Before	532	133	76	380
Change	- 24 u	- 6 u	- 1 u	- 5 u
After	20 p	5 p	4 p	20 p

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

11 b = 209

1 b = 209 ÷ 11 = 19

Number of purple lilies at first
= 7 b
= 7 x 19
= 133

Number of yellow lilies at first
= 4 b
= 4 x 19
= 76

133 - 6 u = 5 p --- (1)

76 - 1 u = 4 p --- (2)

Make p the same.

(1)_x4 
532 - 24 u = 20 p --- (3)

(2)_x5 = (4)
380 - 5 u = 20 p --- (4)

(3) = (4)
532 - 24 u = 380 - 5 u
24 u - 5 u = 532 - 380
19 u = 152

1 u = 152 ÷ 19 = 8

Number of more purple lilies than yellow lilies that she gave away
= 6 u - 1 u
= 5 u
= 5 x 8
= 40

Answer(s): 40