Mrs Lin had a total of 120 yellow and pink carnations in the ratio of 5 : 3. After she had given away 3 times as many yellow carnations as pink carnations, the number of yellow and pink carnations left was in the ratio of 4 : 3. How many more yellow carnations than pink carnations did she give away?

	Yellow	Pink	Total
Before	5 b	3 b	8 b
Change	- 3 u	- 1 u
After	4 p	3 p

	Make p the same (1)x3 = (3)	Yellow (1)	Pink (2)	Make p the same (2)x4 = (4)
Before	225	75	45	180
Change	- 9 u	- 3 u	- 1 u	- 4 u
After	12 p	4 p	3 p	12 p

Number of carnations at first
= 5 b + 3 b
= 8 b

8 b = 120

1 b = 120 ÷ 8 = 15

Number of yellow carnations at first
= 5 b
= 5 x 15
= 75

Number of pink carnations at first
= 3 b
= 3 x 15
= 45

75 - 3 u = 4 p --- (1)

45 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
225 - 9 u = 12 p --- (3)

(2)_x4 = (4)
180 - 4 u = 12 p --- (4)

(3) = (4)
225 - 9 u = 180 - 4 u
9 u - 4 u = 225 - 180
5 u = 45

1 u = 45 ÷ 5 = 9

Number of more yellow carnations than pink carnations that she gave away
= 3 u - 1 u
= 2 u
= 2 x 9
= 18

Answer(s): 18