At first, Ian, John and Valen had the same amount of money. After Valen spent some of his money, Ian spent ²₇ of his money and John spent ¹₂ of his money, Ian had $51 more than John. In the end, the total amount of money the three boys had left was $489. How much money did Valen spend?

	Ian	John	Valen	Total
Before	7x2 =  14 u	2x7 = 14 u	14 u
Change	- 2x2 = - 4 u	- 1x7 = - 7 u	- ?
After	5x2 = 10 u	1x7 = 7 u		$489

The amount that Ian and John each had at first is the same.  Make the amount that they each had the same.  LCM of 7 and 2 is 14.

Amount that Ian had more than John in the end
= 10 u - 7 u
= 3 u

3 u = 51

1 u = 51 ÷ 3 = 17

Amount that Ian and John had in the end
= 10 u + 7 u
= 17 u
= 17 x 17
= $289

Amount that Valen had in the end
= 489 - 289
= $200

Amount that Valen had at first
= 14 u
= 14 x 17
= $238

Amount that Valen spent
= 238 - 200
= $38

Answer(s): $38