Mrs Hun had a total of 90 white and yellow carnations in the ratio of 7 : 3. After she had given away 4 times as many white carnations as yellow carnations, the number of white and yellow carnations left was in the ratio of 7 : 4. How many more white carnations than yellow carnations did she give away?

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

	Make p the same (1)x4 = (3)	White (1)	Yellow (2)	Make p the same (2)x7 = (4)
Before	252	63	27	189
Change	- 16 u	- 4 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 = 90

1 b = 90 ÷ 10 = 9

Number of white carnations at first
= 7 b
= 7 x 9
= 63

Number of yellow carnations at first
= 3 b
= 3 x 9
= 27

63 - 4 u = 7 p --- (1)

27 - 1 u = 4 p --- (2)

Make p the same.

(1)_x4 
252 - 16 u = 28 p --- (3)

(2)_x7 = (4)
189 - 7 u = 28 p --- (4)

(3) = (4)
252 - 16 u = 189 - 7 u
16 u - 7 u = 252 - 189
9 u = 63

1 u = 63 ÷ 9 = 7

Number of more white carnations than yellow carnations that she gave away
= 4 u - 1 u
= 3 u
= 3 x 7
= 21

Answer(s): 21