Mrs Chiam had a total of 130 pink and white roses in the ratio of 7 : 3. After she had given away 6 times as many pink roses as white roses, the number of pink and white roses left was in the ratio of 5 : 3. How many more pink roses than white roses did she give away?

	Pink	White	Total
Before	7 b	3 b	10 b
Change	- 6 u	- 1 u
After	5 p	3 p

	Make p the same (1)x3 = (3)	Pink (1)	White (2)	Make p the same (2)x5 = (4)
Before	273	91	39	195
Change	- 18 u	- 6 u	- 1 u	- 5 u
After	15 p	5 p	3 p	15 p

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

10 b = 130

1 b = 130 ÷ 10 = 13

Number of pink roses at first
= 7 b
= 7 x 13
= 91

Number of white roses at first
= 3 b
= 3 x 13
= 39

91 - 6 u = 5 p --- (1)

39 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
273 - 18 u = 15 p --- (3)

(2)_x5 = (4)
195 - 5 u = 15 p --- (4)

(3) = (4)
273 - 18 u = 195 - 5 u
18 u - 5 u = 273 - 195
13 u = 78

1 u = 78 ÷ 13 = 6

Number of more pink roses than white roses that she gave away
= 6 u - 1 u
= 5 u
= 5 x 6
= 30

Answer(s): 30