Mrs Sher had a total of 140 yellow and pink carnations in the ratio of 5 : 2. After she had given away 5 times as many yellow carnations as pink carnations, the number of yellow and pink carnations left was in the ratio of 5 : 3. How many more yellow carnations than pink carnations did she give away?

	Yellow	Pink	Total
Before	5 b	2 b	7 b
Change	- 5 u	- 1 u
After	5 p	3 p

	Make p the same (1)x3 = (3)	Yellow (1)	Pink (2)	Make p the same (2)x5 = (4)
Before	300	100	40	200
Change	- 15 u	- 5 u	- 1 u	- 5 u
After	15 p	5 p	3 p	15 p

Number of carnations at first
= 5 b + 2 b
= 7 b

7 b = 140

1 b = 140 ÷ 7 = 20

Number of yellow carnations at first
= 5 b
= 5 x 20
= 100

Number of pink carnations at first
= 2 b
= 2 x 20
= 40

100 - 5 u = 5 p --- (1)

40 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
300 - 15 u = 15 p --- (3)

(2)_x5 = (4)
200 - 5 u = 15 p --- (4)

(3) = (4)
300 - 15 u = 200 - 5 u
15 u - 5 u = 300 - 200
10 u = 100

1 u = 100 ÷ 10 = 10

Number of more yellow carnations than pink carnations that she gave away
= 5 u - 1 u
= 4 u
= 4 x 10
= 40

Answer(s): 40