Anna had 20% more coins than Sofia. Isaac had 40% fewer coins than Anna. Anna and Sofia gave Isaac some coins in the ratio of 1 : 5. As a result, Isaac had 50% more coins than before. Given that Sofia had 209 less coins than Isaac in the end, how many coins did Sofia give to Isaac?

Anna	Sofia	Isaac
6x5	5x5
5x6		3x6
30	25	18

100% + 20% = 120%
120% = ¹²⁰₁₀₀ = ⁶₅

Anna : Sofia = 6 : 5

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

Anna : Isaac = 5 : 3

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

	Anna	Sofia	Isaac
Before	30x2 =  60 u	25x2 = 50 u	18x2 = 36 u
Change			+ 9x2 = + 18 u
Comparing the changes in the number of coins	- 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 coins that Anna and Sofia gave to Isaac is repeated.  Make the total number of coins that Anna and Sofia gave to Isaac the same.  LCM of 6 and 9 is 18.

Number of coins that Sofia had less than Isaac 
= 54 u - 35 u
= 19 u

19 u = 209

1 u = 209 ÷ 19 = 11

Number of coins that Sofia gave to Isaac
= 15 u
= 15 x 11
= 165

Answer(s): 165