At first, Riordan, Ivan and Neave had the same amount of money. After Neave spent some of his money, Riordan spent ³₅ of his money and Ivan spent ³₄ of his money, Riordan had $51 more than Ivan. In the end, the total amount of money the three boys had left was $265. How much money did Neave spend?

	Riordan	Ivan	Neave	Total
Before	5x4 =  20 u	4x5 = 20 u	20 u
Change	- 3x4 = - 12 u	- 3x5 = - 15 u	- ?
After	2x4 = 8 u	1x5 = 5 u		$265

The amount that Riordan and Ivan each had at first is the same.  Make the amount that they each had the same.  LCM of 5 and 4 is 20.

Amount that Riordan had more than Ivan in the end
= 8 u - 5 u
= 3 u

3 u = 51

1 u = 51 ÷ 3 = 17

Amount that Riordan and Ivan had in the end
= 8 u + 5 u
= 13 u
= 13 x 17
= $221

Amount that Neave had in the end
= 265 - 221
= $44

Amount that Neave had at first
= 20 u
= 20 x 17
= $340

Amount that Neave spent
= 340 - 44
= $296

Answer(s): $296