Luke, Harry, Gabriel and Julian shared $360. Julian received ⁴₅ of the total amount of money received by Luke, Harry and Gabriel. Luke received ¹₃ of the total amount for Harry and Gabriel. Harry received ²₃ as much money as Gabriel. If Harry gave all his money to Julian, how much did Julian have more than Luke in the end?

Luke	Harry	Gabriel	Julian	Total
5x4			4x4	9x4
1x5	3x5
	2x3	3x3
5 u	6 u	9 u	16 u	36 u

The total amount that Harry and Gabriel have is repeated.  Make the total amount of Harry and Gabriel the same.  LCM of 5 and 3 is 15.

The total amount that Luke, Harry and Gabriel have is repeated.  Make the total amount of Luke, Harry and Gabriel the same. LCM of 20 and 5 is 20.

Total amount that Luke, Harry, Gabriel and Julian shared = 36 u

36 u = 360

1 u = 360 ÷ 36 = 10

	Luke	Harry	Gabriel	Julian
Before	5 u	6 u	9 u	16 u
Change		- 6 u		+ 6 u
After	5 u	0 u	9 u	22 u

Amount that Julian had if Harry gave him all his money
= 16 u + 6 u
= 22 u

Amount that Julian had more than Luke
= 22 u - 5 u
= 17 u
= 17 x 10
= $170

Answer(s): $170