Mrs Lim had a total of 90 purple and yellow roses in the ratio of 7 : 2. After she had given away 5 times as many purple roses as yellow roses, the number of purple and yellow roses left was in the ratio of 5 : 2. How many more purple roses than yellow roses did she give away?

	Purple	Yellow	Total
Before	7 b	2 b	9 b
Change	- 5 u	- 1 u
After	5 p	2 p

	Make p the same (1)x2 = (3)	Purple (1)	Yellow (2)	Make p the same (2)x5 = (4)
Before	140	70	20	100
Change	- 10 u	- 5 u	- 1 u	- 5 u
After	10 p	5 p	2 p	10 p

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

9 b = 90

1 b = 90 ÷ 9 = 10

Number of purple roses at first
= 7 b
= 7 x 10
= 70

Number of yellow roses at first
= 2 b
= 2 x 10
= 20

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

20 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
140 - 10 u = 10 p --- (3)

(2)_x5 = (4)
100 - 5 u = 10 p --- (4)

(3) = (4)
140 - 10 u = 100 - 5 u
10 u - 5 u = 140 - 100
5 u = 40

1 u = 40 ÷ 5 = 8

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

Answer(s): 32