Mrs Ma had a total of 117 purple and pink carnations in the ratio of 10 : 3. After she had given away 4 times as many purple carnations as pink carnations, the number of purple and pink carnations left was in the ratio of 5 : 2. How many more purple carnations than pink carnations did she give away?

	Purple	Pink	Total
Before	10 b	3 b	13 b
Change	- 4 u	- 1 u
After	5 p	2 p

	Make p the same (1)x2 = (3)	Purple (1)	Pink (2)	Make p the same (2)x5 = (4)
Before	180	90	27	135
Change	- 8 u	- 4 u	- 1 u	- 5 u
After	10 p	5 p	2 p	10 p

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

13 b = 117

1 b = 117 ÷ 13 = 9

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

Number of pink carnations at first
= 3 b
= 3 x 9
= 27

90 - 4 u = 5 p --- (1)

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

Make p the same.

(1)_x2 
180 - 8 u = 10 p --- (3)

(2)_x5 = (4)
135 - 5 u = 10 p --- (4)

(3) = (4)
180 - 8 u = 135 - 5 u
8 u - 5 u = 180 - 135
3 u = 45

1 u = 45 ÷ 3 = 15

Number of more purple carnations than pink carnations that she gave away
= 4 u - 1 u
= 3 u
= 3 x 15
= 45

Answer(s): 45