Mrs Sim had a total of 182 purple and yellow daisies in the ratio of 8 : 5. After she had given away 4 times as many purple daisies as yellow daisies, the number of purple and yellow daisies left was in the ratio of 4 : 3. How many more purple daisies than yellow daisies did she give away?

	Purple	Yellow	Total
Before	8 b	5 b	13 b
Change	- 4 u	- 1 u
After	4 p	3 p

	Make p the same (1)x3 = (3)	Purple (1)	Yellow (2)	Make p the same (2)x4 = (4)
Before	336	112	70	280
Change	- 12 u	- 4 u	- 1 u	- 4 u
After	12 p	4 p	3 p	12 p

Number of daisies at first
= 8 b + 5 b
= 13 b

13 b = 182

1 b = 182 ÷ 13 = 14

Number of purple daisies at first
= 8 b
= 8 x 14
= 112

Number of yellow daisies at first
= 5 b
= 5 x 14
= 70

112 - 4 u = 4 p --- (1)

70 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
336 - 12 u = 12 p --- (3)

(2)_x4 = (4)
280 - 4 u = 12 p --- (4)

(3) = (4)
336 - 12 u = 280 - 4 u
12 u - 4 u = 336 - 280
8 u = 56

1 u = 56 ÷ 8 = 7

Number of more purple daisies than yellow daisies that she gave away
= 4 u - 1 u
= 3 u
= 3 x 7
= 21

Answer(s): 21