Aaron had 20% more coins than Jacob. Henry had 40% fewer coins than Aaron. Aaron and Jacob gave Henry some coins in the ratio of 1 : 5. As a result, Henry had 50% more coins than before. Given that Henry had 76 more coins than Jacob in the end, how many coins did Aaron give to Henry?

Aaron	Jacob	Henry
6x5	5x5
5x6		3x6
30	25	18

100% + 20% = 120%
120% = ¹²⁰₁₀₀ = ⁶₅

Aaron : Jacob = 6 : 5

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

Aaron : Henry = 5 : 3

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

	Aaron	Jacob	Henry
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 Aaron and Jacob gave to Henry is repeated.  Make the total number of coins that Aaron and Jacob gave to Henry the same.  LCM of 6 and 9 is 18.

Number of coins that Henry had more than Jacob 
= 54 u - 35 u
= 19 u

19 u = 76

1 u = 76 ÷ 19 = 4

Number of coins that Aaron gave to Henry
= 3 u
= 3 x 4
= 12

Answer(s): 12