Jeremy, Liam and Daniel had some marbles. Liam had 40% less marbles than Jeremy. Liam had ²₅ of Daniel's. After Jeremy gave 242 marbles to Liam, he had ¹₅ of what Liam had. How many more marbles did Daniel have than Jeremy in the end?

Jeremy	Liam	Daniel
5x2	3x2
	2x3	5x3
10	6	15

	Daniel	Jeremy	Liam	Total marbles of  Jeremy and Liam
Before	15x3 = 45 u	10x3 = 30 u	6x3 = 18 u	16x3 = 48 u
Change		- 242	+ 242
After	45 u	1x8 = 8 u	5x8 = 40 u	6x8 = 48 u

Number of marbles that Liam had less than Jeremy at first in percent
= 100% - 40%
= 60%

60% = ⁶⁰₁₀₀ = ³₅

Jeremy : Liam = 5 : 3

The number of marbles that Liam had at first is repeated.  Make the number of marbles that Liam had at first the same.  LCM of 3 and 2 is 6.

When Jeremy gave 242 marbles to Liam, the total number of marbles that Liam and Jeremy had at first and in the end remains the same.  Make the total number of marbles that Liam and Jeremy had the same.  LCM of 16 and 6 is 48.

Number of marbles that Jeremy gave to Liam
= 30 u - 8 u
= 22 u

22 u = 242

1 u = 242 ÷ 22 = 11

Number of marbles that Daniel had more than Jeremy in the end
= 45 u - 8 u
= 37 u
= 37 x 11
= 407

Answer(s): 407