Ben, Liam, Ethan and Michael shared $245. Michael received ³₄ of the total amount of money received by Ben, Liam and Ethan. Ben received ²₃ of the total amount for Liam and Ethan. Liam received ¹₃ as much money as Ethan. If Ethan gave all his money to Michael, how much did Michael have more than Liam in the end?

Ben	Liam	Ethan	Michael	Total
4x5			3x5	7x5
2x4	3x4
	1x3	3x3
8 u	3 u	9 u	15 u	35 u

The total amount that Liam and Ethan have is repeated.  Make the total amount of Liam and Ethan the same.  LCM of 4 and 3 is 12.

The total amount that Ben, Liam and Ethan have is repeated.  Make the total amount of Ben, Liam and Ethan the same. LCM of 20 and 4 is 20.

Total amount that Ben, Liam, Ethan and Michael shared = 35 u

35 u = 245

1 u = 245 ÷ 35 = 7

	Ben	Liam	Ethan	Michael
Before	8 u	3 u	9 u	15 u
Change			- 9 u	+ 9 u
After	8 u	3 u	0 u	24 u

Amount that Michael had if Ethan gave him all his money
= 15 u + 9 u
= 24 u

Amount that Michael had more than Liam
= 24 u - 3 u
= 21 u
= 21 x 7
= $147

Answer(s): $147