At first, Elijah, Nick and Cole had the same amount of money. After Cole spent some of his money, Elijah spent ³₇ of his money and Nick spent ²₃ of his money, Elijah had $50 more than Nick. In the end, the total amount of money the three boys had left was $345. How much money did Cole spend?

	Elijah	Nick	Cole	Total
Before	7x3 =  21 u	3x7 = 21 u	21 u
Change	- 3x3 = - 9 u	- 2x7 = - 14 u	- ?
After	4x3 = 12 u	1x7 = 7 u		$345

The amount that Elijah and Nick each had at first is the same.  Make the amount that they each had the same.  LCM of 7 and 3 is 21.

Amount that Elijah had more than Nick in the end
= 12 u - 7 u
= 5 u

5 u = 50

1 u = 50 ÷ 5 = 10

Amount that Elijah and Nick had in the end
= 12 u + 7 u
= 19 u
= 19 x 10
= $190

Amount that Cole had in the end
= 345 - 190
= $155

Amount that Cole had at first
= 21 u
= 21 x 10
= $210

Amount that Cole spent
= 210 - 155
= $55

Answer(s): $55