Mrs Lau had a total of 130 yellow and pink roses in the ratio of 9 : 4. After she had given away 4 times as many yellow roses as pink roses, the number of yellow and pink roses left was in the ratio of 6 : 5. How many more yellow roses than pink roses did she give away?

	Yellow	Pink	Total
Before	9 b	4 b	13 b
Change	- 4 u	- 1 u
After	6 p	5 p

	Make p the same (1)x5 = (3)	Yellow (1)	Pink (2)	Make p the same (2)x6 = (4)
Before	450	90	40	240
Change	- 20 u	- 4 u	- 1 u	- 6 u
After	30 p	6 p	5 p	30 p

Number of roses at first
= 9 b + 4 b
= 13 b

13 b = 130

1 b = 130 ÷ 13 = 10

Number of yellow roses at first
= 9 b
= 9 x 10
= 90

Number of pink roses at first
= 4 b
= 4 x 10
= 40

90 - 4 u = 6 p --- (1)

40 - 1 u = 5 p --- (2)

Make p the same.

(1)_x5 
450 - 20 u = 30 p --- (3)

(2)_x6 = (4)
240 - 6 u = 30 p --- (4)

(3) = (4)
450 - 20 u = 240 - 6 u
20 u - 6 u = 450 - 240
14 u = 210

1 u = 210 ÷ 14 = 15

Number of more yellow roses than pink roses that she gave away
= 4 u - 1 u
= 3 u
= 3 x 15
= 45

Answer(s): 45