Mrs Ang had a total of 70 purple and white tulips in the ratio of 9 : 5. After she had given away 4 times as many purple tulips as white tulips, the number of purple and white tulips left was in the ratio of 5 : 4. How many more purple tulips than white tulips did she give away?

	Purple	White	Total
Before	9 b	5 b	14 b
Change	- 4 u	- 1 u
After	5 p	4 p

	Make p the same (1)x4 = (3)	Purple (1)	White (2)	Make p the same (2)x5 = (4)
Before	180	45	25	125
Change	- 16 u	- 4 u	- 1 u	- 5 u
After	20 p	5 p	4 p	20 p

Number of tulips at first
= 9 b + 5 b
= 14 b

14 b = 70

1 b = 70 ÷ 14 = 5

Number of purple tulips at first
= 9 b
= 9 x 5
= 45

Number of white tulips at first
= 5 b
= 5 x 5
= 25

45 - 4 u = 5 p --- (1)

25 - 1 u = 4 p --- (2)

Make p the same.

(1)_x4 
180 - 16 u = 20 p --- (3)

(2)_x5 = (4)
125 - 5 u = 20 p --- (4)

(3) = (4)
180 - 16 u = 125 - 5 u
16 u - 5 u = 180 - 125
11 u = 55

1 u = 55 ÷ 11 = 5

Number of more purple tulips than white tulips that she gave away
= 4 u - 1 u
= 3 u
= 3 x 5
= 15

Answer(s): 15