Mrs Lau had a total of 176 pink and white carnations in the ratio of 9 : 2. After she had given away 6 times as many pink carnations as white carnations, the number of pink and white carnations left was in the ratio of 10 : 3. How many more pink carnations than white carnations did she give away?

	Pink	White	Total
Before	9 b	2 b	11 b
Change	- 6 u	- 1 u
After	10 p	3 p

	Make p the same (1)x3 = (3)	Pink (1)	White (2)	Make p the same (2)x10 = (4)
Before	432	144	32	320
Change	- 18 u	- 6 u	- 1 u	- 10 u
After	30 p	10 p	3 p	30 p

Number of carnations at first
= 9 b + 2 b
= 11 b

11 b = 176

1 b = 176 ÷ 11 = 16

Number of pink carnations at first
= 9 b
= 9 x 16
= 144

Number of white carnations at first
= 2 b
= 2 x 16
= 32

144 - 6 u = 10 p --- (1)

32 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
432 - 18 u = 30 p --- (3)

(2)_x10 = (4)
320 - 10 u = 30 p --- (4)

(3) = (4)
432 - 18 u = 320 - 10 u
18 u - 10 u = 432 - 320
8 u = 112

1 u = 112 ÷ 8 = 14

Number of more pink carnations than white carnations that she gave away
= 6 u - 1 u
= 5 u
= 5 x 14
= 70

Answer(s): 70