Mrs Koh had a total of 117 purple and white tulips in the ratio of 10 : 3. After she had given away 6 times as many purple tulips as white tulips, the number of purple and white tulips left was in the ratio of 6 : 5. How many more purple tulips than white tulips did she give away?

	Purple	White	Total
Before	10 b	3 b	13 b
Change	- 6 u	- 1 u
After	6 p	5 p

	Make p the same (1)x5 = (3)	Purple (1)	White (2)	Make p the same (2)x6 = (4)
Before	450	90	27	162
Change	- 30 u	- 6 u	- 1 u	- 6 u
After	30 p	6 p	5 p	30 p

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

13 b = 117

1 b = 117 ÷ 13 = 9

Number of purple tulips at first
= 10 b
= 10 x 9
= 90

Number of white tulips at first
= 3 b
= 3 x 9
= 27

90 - 6 u = 6 p --- (1)

27 - 1 u = 5 p --- (2)

Make p the same.

(1)_x5 
450 - 30 u = 30 p --- (3)

(2)_x6 = (4)
162 - 6 u = 30 p --- (4)

(3) = (4)
450 - 30 u = 162 - 6 u
30 u - 6 u = 450 - 162
24 u = 288

1 u = 288 ÷ 24 = 12

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

Answer(s): 60