Mrs Ng had a total of 112 pink and purple roses in the ratio of 5 : 2. After she had given away 5 times as many pink roses as purple roses, the number of pink and purple roses left was in the ratio of 5 : 3. How many more pink roses than purple roses did she give away?

	Pink	Purple	Total
Before	5 b	2 b	7 b
Change	- 5 u	- 1 u
After	5 p	3 p

	Make p the same (1)x3 = (3)	Pink (1)	Purple (2)	Make p the same (2)x5 = (4)
Before	240	80	32	160
Change	- 15 u	- 5 u	- 1 u	- 5 u
After	15 p	5 p	3 p	15 p

Number of roses at first
= 5 b + 2 b
= 7 b

7 b = 112

1 b = 112 ÷ 7 = 16

Number of pink roses at first
= 5 b
= 5 x 16
= 80

Number of purple roses at first
= 2 b
= 2 x 16
= 32

80 - 5 u = 5 p --- (1)

32 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
240 - 15 u = 15 p --- (3)

(2)_x5 = (4)
160 - 5 u = 15 p --- (4)

(3) = (4)
240 - 15 u = 160 - 5 u
15 u - 5 u = 240 - 160
10 u = 80

1 u = 80 ÷ 10 = 8

Number of more pink roses than purple roses that she gave away
= 5 u - 1 u
= 4 u
= 4 x 8
= 32

Answer(s): 32