Mrs Chen had a total of 165 purple and yellow tulips in the ratio of 8 : 3. After she had given away 4 times as many purple tulips as yellow tulips, the number of purple and yellow tulips left was in the ratio of 5 : 2. How many more purple tulips than yellow tulips did she give away?

	Purple	Yellow	Total
Before	8 b	3 b	11 b
Change	- 4 u	- 1 u
After	5 p	2 p

	Make p the same (1)x2 = (3)	Purple (1)	Yellow (2)	Make p the same (2)x5 = (4)
Before	240	120	45	225
Change	- 8 u	- 4 u	- 1 u	- 5 u
After	10 p	5 p	2 p	10 p

Number of tulips at first
= 8 b + 3 b
= 11 b

11 b = 165

1 b = 165 ÷ 11 = 15

Number of purple tulips at first
= 8 b
= 8 x 15
= 120

Number of yellow tulips at first
= 3 b
= 3 x 15
= 45

120 - 4 u = 5 p --- (1)

45 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
240 - 8 u = 10 p --- (3)

(2)_x5 = (4)
225 - 5 u = 10 p --- (4)

(3) = (4)
240 - 8 u = 225 - 5 u
8 u - 5 u = 240 - 225
3 u = 15

1 u = 15 ÷ 3 = 5

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

Answer(s): 15