Mrs Song had a total of 140 pink and yellow carnations in the ratio of 7 : 3. After she had given away 4 times as many pink carnations as yellow carnations, the number of pink and yellow carnations left was in the ratio of 3 : 2. How many more pink carnations than yellow carnations did she give away?

	Pink	Yellow	Total
Before	7 b	3 b	10 b
Change	- 4 u	- 1 u
After	3 p	2 p

	Make p the same (1)x2 = (3)	Pink (1)	Yellow (2)	Make p the same (2)x3 = (4)
Before	196	98	42	126
Change	- 8 u	- 4 u	- 1 u	- 3 u
After	6 p	3 p	2 p	6 p

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

10 b = 140

1 b = 140 ÷ 10 = 14

Number of pink carnations at first
= 7 b
= 7 x 14
= 98

Number of yellow carnations at first
= 3 b
= 3 x 14
= 42

98 - 4 u = 3 p --- (1)

42 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
196 - 8 u = 6 p --- (3)

(2)_x3 = (4)
126 - 3 u = 6 p --- (4)

(3) = (4)
196 - 8 u = 126 - 3 u
8 u - 3 u = 196 - 126
5 u = 70

1 u = 70 ÷ 5 = 14

Number of more pink carnations than yellow carnations that she gave away
= 4 u - 1 u
= 3 u
= 3 x 14
= 42

Answer(s): 42