Samuel had 20% more stickers than Mason. Lily had 40% fewer stickers than Samuel. Samuel and Mason gave Lily some stickers in the ratio of 1 : 5. As a result, Lily had 50% more stickers than before. Given that Lily had 209 more stickers than Mason in the end, how many stickers did Samuel give to Lily?

Samuel	Mason	Lily
6x5	5x5
5x6		3x6
30	25	18

100% + 20% = 120%
120% = ¹²⁰₁₀₀ = ⁶₅

Samuel : Mason = 6 : 5

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

Samuel : Lily = 5 : 3

The number of stickers that Samuel had at first is repeated. Make the number of stickers that Samuel had at first the same.  LCM of 6 and 5 is 30.

	Samuel	Mason	Lily
Before	30x2 =  60 u	25x2 = 50 u	18x2 = 36 u
Change			+ 9x2 = + 18 u
Comparing the changes in the number of stickers	- 1x3 = - 3 u	- 5x3 = - 15 u	+ 6x3 = + 18 u
After	57 u	35 u	27x2 = 54 u

50% x 18 
= ⁵⁰₁₀₀ x 18 
= 9 

The total number of stickers that Samuel and Mason gave to Lily is repeated.  Make the total number of stickers that Samuel and Mason gave to Lily the same.  LCM of 6 and 9 is 18.

Number of stickers that Lily had more than Mason 
= 54 u - 35 u
= 19 u

19 u = 209

1 u = 209 ÷ 19 = 11

Number of stickers that Samuel gave to Lily
= 3 u
= 3 x 11
= 33

Answer(s): 33