Mrs Loo had a total of 117 yellow and white carnations in the ratio of 9 : 4. After she had given away 5 times as many yellow carnations as white carnations, the number of yellow and white carnations left was in the ratio of 4 : 3. How many more yellow carnations than white carnations did she give away?

	Yellow	White	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)	Yellow (1)	White (2)	Make p the same (2)x4 = (4)
Before	243	81	36	144
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 = 117

1 b = 117 ÷ 13 = 9

Number of yellow carnations at first
= 9 b
= 9 x 9
= 81

Number of white carnations at first
= 4 b
= 4 x 9
= 36

81 - 5 u = 4 p --- (1)

36 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
243 - 15 u = 12 p --- (3)

(2)_x4 = (4)
144 - 4 u = 12 p --- (4)

(3) = (4)
243 - 15 u = 144 - 4 u
15 u - 4 u = 243 - 144
11 u = 99

1 u = 99 ÷ 11 = 9

Number of more yellow carnations than white carnations that she gave away
= 5 u - 1 u
= 4 u
= 4 x 9
= 36

Answer(s): 36