Mrs Chen had a total of 72 yellow and white roses in the ratio of 7 : 2. After she had given away 4 times as many yellow roses as white roses, the number of yellow and white roses left was in the ratio of 4 : 3. How many more yellow roses than white roses did she give away?

	Yellow	White	Total
Before	7 b	2 b	9 b
Change	- 4 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	168	56	16	64
Change	- 12 u	- 4 u	- 1 u	- 4 u
After	12 p	4 p	3 p	12 p

Number of roses at first
= 7 b + 2 b
= 9 b

9 b = 72

1 b = 72 ÷ 9 = 8

Number of yellow roses at first
= 7 b
= 7 x 8
= 56

Number of white roses at first
= 2 b
= 2 x 8
= 16

56 - 4 u = 4 p --- (1)

16 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
168 - 12 u = 12 p --- (3)

(2)_x4 = (4)
64 - 4 u = 12 p --- (4)

(3) = (4)
168 - 12 u = 64 - 4 u
12 u - 4 u = 168 - 64
8 u = 104

1 u = 104 ÷ 8 = 13

Number of more yellow roses than white roses that she gave away
= 4 u - 1 u
= 3 u
= 3 x 13
= 39

Answer(s): 39