Mrs Heng had a total of 130 pink and purple carnations in the ratio of 7 : 3. After she had given away 5 times as many pink carnations as purple carnations, the number of pink and purple carnations left was in the ratio of 7 : 4. How many more pink carnations than purple carnations did she give away?

	Pink	Purple	Total
Before	7 b	3 b	10 b
Change	- 5 u	- 1 u
After	7 p	4 p

	Make p the same (1)x4 = (3)	Pink (1)	Purple (2)	Make p the same (2)x7 = (4)
Before	364	91	39	273
Change	- 20 u	- 5 u	- 1 u	- 7 u
After	28 p	7 p	4 p	28 p

Number of carnations at first
= 7 b + 3 b
= 10 b

10 b = 130

1 b = 130 ÷ 10 = 13

Number of pink carnations at first
= 7 b
= 7 x 13
= 91

Number of purple carnations at first
= 3 b
= 3 x 13
= 39

91 - 5 u = 7 p --- (1)

39 - 1 u = 4 p --- (2)

Make p the same.

(1)_x4 
364 - 20 u = 28 p --- (3)

(2)_x7 = (4)
273 - 7 u = 28 p --- (4)

(3) = (4)
364 - 20 u = 273 - 7 u
20 u - 7 u = 364 - 273
13 u = 91

1 u = 91 ÷ 13 = 7

Number of more pink carnations than purple carnations that she gave away
= 5 u - 1 u
= 4 u
= 4 x 7
= 28

Answer(s): 28