Mrs Pang had a total of 100 yellow and white carnations in the ratio of 7 : 3. 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 5 : 3. How many more yellow carnations than white carnations did she give away?

	Yellow	White	Total
Before	7 b	3 b	10 b
Change	- 5 u	- 1 u
After	5 p	3 p

	Make p the same (1)x3 = (3)	Yellow (1)	White (2)	Make p the same (2)x5 = (4)
Before	210	70	30	150
Change	- 15 u	- 5 u	- 1 u	- 5 u
After	15 p	5 p	3 p	15 p

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

10 b = 100

1 b = 100 ÷ 10 = 10

Number of yellow carnations at first
= 7 b
= 7 x 10
= 70

Number of white carnations at first
= 3 b
= 3 x 10
= 30

70 - 5 u = 5 p --- (1)

30 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
210 - 15 u = 15 p --- (3)

(2)_x5 = (4)
150 - 5 u = 15 p --- (4)

(3) = (4)
210 - 15 u = 150 - 5 u
15 u - 5 u = 210 - 150
10 u = 60

1 u = 60 ÷ 10 = 6

Number of more yellow carnations than white carnations that she gave away
= 5 u - 1 u
= 4 u
= 4 x 6
= 24

Answer(s): 24