Mrs Sher had a total of 182 purple and yellow carnations in the ratio of 9 : 4. After she had given away 5 times as many purple carnations as yellow carnations, the number of purple and yellow carnations left was in the ratio of 4 : 3. How many more purple carnations than yellow carnations did she give away?

	Purple	Yellow	Total
Before	9 b	4 b	13 b
Change	- 5 u	- 1 u
After	4 p	3 p

	Make p the same (1)x3 = (3)	Purple (1)	Yellow (2)	Make p the same (2)x4 = (4)
Before	378	126	56	224
Change	- 15 u	- 5 u	- 1 u	- 4 u
After	12 p	4 p	3 p	12 p

Number of carnations at first
= 9 b + 4 b
= 13 b

13 b = 182

1 b = 182 ÷ 13 = 14

Number of purple carnations at first
= 9 b
= 9 x 14
= 126

Number of yellow carnations at first
= 4 b
= 4 x 14
= 56

126 - 5 u = 4 p --- (1)

56 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
378 - 15 u = 12 p --- (3)

(2)_x4 = (4)
224 - 4 u = 12 p --- (4)

(3) = (4)
378 - 15 u = 224 - 4 u
15 u - 4 u = 378 - 224
11 u = 154

1 u = 154 ÷ 11 = 14

Number of more purple carnations than yellow carnations that she gave away
= 5 u - 1 u
= 4 u
= 4 x 14
= 56

Answer(s): 56