Pierre, John, Luis and Vincent shared $396. Vincent received ⁴₅ of the total amount of money received by Pierre, John and Luis. Pierre received ¹₃ of the total amount for John and Luis. John received ²₃ as much money as Luis. If Luis gave all his money to Vincent, how much did Vincent have more than John in the end?

Pierre	John	Luis	Vincent	Total
5x4			4x4	9x4
1x5	3x5
	2x3	3x3
5 u	6 u	9 u	16 u	36 u

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

The total amount that Pierre, John and Luis have is repeated.  Make the total amount of Pierre, John and Luis the same. LCM of 20 and 5 is 20.

Total amount that Pierre, John, Luis and Vincent shared = 36 u

36 u = 396

1 u = 396 ÷ 36 = 11

	Pierre	John	Luis	Vincent
Before	5 u	6 u	9 u	16 u
Change			- 9 u	+ 9 u
After	5 u	6 u	0 u	25 u

Amount that Vincent had if Luis gave him all his money
= 16 u + 9 u
= 25 u

Amount that Vincent had more than John
= 25 u - 6 u
= 19 u
= 19 x 11
= $209

Answer(s): $209