Mrs Tan had a total of 162 purple and yellow roses in the ratio of 7 : 2. After she had given away 4 times as many purple roses as yellow roses, the number of purple and yellow roses left was in the ratio of 10 : 3. How many more purple roses than yellow roses did she give away?

	Purple	Yellow	Total
Before	7 b	2 b	9 b
Change	- 4 u	- 1 u
After	10 p	3 p

	Make p the same (1)x3 = (3)	Purple (1)	Yellow (2)	Make p the same (2)x10 = (4)
Before	378	126	36	360
Change	- 12 u	- 4 u	- 1 u	- 10 u
After	30 p	10 p	3 p	30 p

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

9 b = 162

1 b = 162 ÷ 9 = 18

Number of purple roses at first
= 7 b
= 7 x 18
= 126

Number of yellow roses at first
= 2 b
= 2 x 18
= 36

126 - 4 u = 10 p --- (1)

36 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
378 - 12 u = 30 p --- (3)

(2)_x10 = (4)
360 - 10 u = 30 p --- (4)

(3) = (4)
378 - 12 u = 360 - 10 u
12 u - 10 u = 378 - 360
2 u = 18

1 u = 18 ÷ 2 = 9

Number of more purple roses than yellow roses that she gave away
= 4 u - 1 u
= 3 u
= 3 x 9
= 27

Answer(s): 27