Gabriel, Rael and David had some marbles. Rael had 60% less marbles than Gabriel. Rael had ³₇ of David's. After Gabriel gave 230 marbles to Rael, he had ¹₅ of what Rael had. How many more marbles did David have than Gabriel in the end?

Gabriel	Rael	David
5x3	2x3
	3x2	7x2
15	6	14

	David	Gabriel	Rael	Total marbles of  Gabriel and Rael
Before	14x2 = 28 u	15x2 = 30 u	6x2 = 12 u	21x2 = 42 u
Change		- 230	+ 230
After	28 u	1x7 = 7 u	5x7 = 35 u	6x7 = 42 u

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

40% = ⁴⁰₁₀₀ = ²₅

Gabriel : Rael = 5 : 2

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

When Gabriel gave 230 marbles to Rael, the total number of marbles that Rael and Gabriel had at first and in the end remains the same.  Make the total number of marbles that Rael and Gabriel had the same.  LCM of 21 and 6 is 42.

Number of marbles that Gabriel gave to Rael
= 30 u - 7 u
= 23 u

23 u = 230

1 u = 230 ÷ 23 = 10

Number of marbles that David had more than Gabriel in the end
= 28 u - 7 u
= 21 u
= 21 x 10
= 210

Answer(s): 210