Mrs Hun had a total of 165 white and pink roses in the ratio of 8 : 3. After she had given away 5 times as many white roses as pink roses, the number of white and pink roses left was in the ratio of 3 : 2. How many more white roses than pink roses did she give away?

	White	Pink	Total
Before	8 b	3 b	11 b
Change	- 5 u	- 1 u
After	3 p	2 p

	Make p the same (1)x2 = (3)	White (1)	Pink (2)	Make p the same (2)x3 = (4)
Before	240	120	45	135
Change	- 10 u	- 5 u	- 1 u	- 3 u
After	6 p	3 p	2 p	6 p

Number of roses at first
= 8 b + 3 b
= 11 b

11 b = 165

1 b = 165 ÷ 11 = 15

Number of white roses at first
= 8 b
= 8 x 15
= 120

Number of pink roses at first
= 3 b
= 3 x 15
= 45

120 - 5 u = 3 p --- (1)

45 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
240 - 10 u = 6 p --- (3)

(2)_x3 = (4)
135 - 3 u = 6 p --- (4)

(3) = (4)
240 - 10 u = 135 - 3 u
10 u - 3 u = 240 - 135
7 u = 105

1 u = 105 ÷ 7 = 15

Number of more white roses than pink roses that she gave away
= 5 u - 1 u
= 4 u
= 4 x 15
= 60

Answer(s): 60