Mrs Pang had a total of 152 yellow and pink roses in the ratio of 5 : 3. After she had given away 6 times as many yellow roses as pink roses, the number of yellow and pink roses left was in the ratio of 5 : 4. How many more yellow roses than pink roses did she give away?

	Yellow	Pink	Total
Before	5 b	3 b	8 b
Change	- 6 u	- 1 u
After	5 p	4 p

	Make p the same (1)x4 = (3)	Yellow (1)	Pink (2)	Make p the same (2)x5 = (4)
Before	380	95	57	285
Change	- 24 u	- 6 u	- 1 u	- 5 u
After	20 p	5 p	4 p	20 p

Number of roses at first
= 5 b + 3 b
= 8 b

8 b = 152

1 b = 152 ÷ 8 = 19

Number of yellow roses at first
= 5 b
= 5 x 19
= 95

Number of pink roses at first
= 3 b
= 3 x 19
= 57

95 - 6 u = 5 p --- (1)

57 - 1 u = 4 p --- (2)

Make p the same.

(1)_x4 
380 - 24 u = 20 p --- (3)

(2)_x5 = (4)
285 - 5 u = 20 p --- (4)

(3) = (4)
380 - 24 u = 285 - 5 u
24 u - 5 u = 380 - 285
19 u = 95

1 u = 95 ÷ 19 = 5

Number of more yellow roses than pink roses that she gave away
= 6 u - 1 u
= 5 u
= 5 x 5
= 25

Answer(s): 25