Samuel bought 50% more marbles than Isaiah. Jack bought 35% fewer marbles than Samuel. Samuel and Isaiah gave Jack some marbles in the ratio 2 : 1. As a result, Jack had twice as much marbles as before. Given that Samuel had 60 less marbles than Isaiah in the end, how much marbles did Samuel and Isaiah give to Jack?

	Samuel	Isaiah	Jack
	3x20	2x20
	20x3		13x3
Before	60 u	40 u	39 u
Change			+ (2 x 39 u) = + 78 u
	- 2x26 = - 52 u	- 1x26 = - 26 u	+ 3x26 =  + 78 u
After	8 u	14 u	117 u

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

100% - 35% = 65%
65% = ⁶⁵₁₀₀ = ¹³₂₀

The number of marbles that Samuel had at first is the repeated identity.
LCM of 3 and 20 = 60

The change in the number of marbles that Jack had is the repeated identity when Samuel and Isaiah gave to Jack.
LCM of 78 and 3 = 78

Number of marbles that Samuel had less than Isaiah in the end
= 14 u - 8 u
= 6 u

6 u = 60
1 u = 60 ÷ 6 = 10

Number of marbles that Samuel and Isaiah gave to Jack
= 52 u + 26 u
= 78 u
= 78 x 10
= 780

Answer(s): 780