Liam, Reggie and Paul had some marbles. Reggie had 40% more marbles than Liam. Reggie had ³₇ of Paul's. After Liam gave 108 marbles to Reggie, he had ¹₅ of what Reggie had. How many more marbles did Paul have than Reggie in the end?

Liam	Reggie	Paul
5x3	7x3
	3x7	7x7
15	21	49

	Paul	Liam	Reggie	Total marbles of  Liam and Reggie
Before	49x1 = 49 u	15x1 = 15 u	21x1 = 21 u	36x1 = 36 u
Change		- 108	+ 108
After	49 u	1x6 = 6 u	5x6 = 30 u	6x6 = 36 u

Number of marbles that Reggie had more than Liam at first in percent
= 100%+ 40%
= 140%

140% = ¹⁴⁰₁₀₀ = ⁷₅

Liam : Reggie = 5 : 7

The number of marbles that Reggie had at first is repeated.  Make the number of marbles that Reggie had at first the same.  LCM of 7 and 3 is 21.

When Liam gave 108 marbles to Reggie, the total number of marbles that Reggie and Liam had at first and in the end remains the same.  Make the total number of marbles that Reggie and Liam had the same.  LCM of 36 and 6 is 36.

Number of marbles that Liam gave to Reggie
= 15 u - 6 u
= 9 u

9 u = 108

1 u = 108 ÷ 9 = 12

Number of marbles that Paul had more than Reggie in the end
= 49 u - 30 u
= 19 u
= 19 x 12
= 228

Answer(s): 228