Lucas had 40% more coins than Luke. Levi had 20% fewer coins than Lucas. Lucas and Luke gave Levi some coins in the ratio of 3 : 4. As a result, Levi had 50% more coins than before. Given that Levi had 150 more coins than Luke in the end, how many coins did Lucas give to Levi?

Lucas	Luke	Levi
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

Lucas : Luke = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Lucas : Levi = 5 : 4

The number of coins that Lucas had at first is repeated. Make the number of coins that Lucas had at first the same.  LCM of 7 and 5 is 35.

	Lucas	Luke	Levi
Before	35x1 =  35 u	25x1 = 25 u	28x1 = 28 u
Change			+ 14x1 = + 14 u
Comparing the changes in the number of coins	- 3x2 = - 6 u	- 4x2 = - 8 u	+ 7x2 = + 14 u
After	29 u	17 u	42x1 = 42 u

50% x 28 
= ⁵⁰₁₀₀ x 28 
= 14 

The total number of coins that Lucas and Luke gave to Levi is repeated.  Make the total number of coins that Lucas and Luke gave to Levi the same.  LCM of 7 and 14 is 14.

Number of coins that Levi had more than Luke 
= 42 u - 17 u
= 25 u

25 u = 150

1 u = 150 ÷ 25 = 6

Number of coins that Lucas gave to Levi
= 6 u
= 6 x 6
= 36

Answer(s): 36