At first, Japheth, Jeremy and Zeph had the same amount of money. After Zeph spent some of his money, Japheth spent ³₈ of his money and Jeremy spent ³₄ of his money, Japheth had $42 more than Jeremy. In the end, the total amount of money the three boys had left was $174. How much money did Zeph spend?

	Japheth	Jeremy	Zeph	Total
Before	8x1 =  8 u	4x2 = 8 u	8 u
Change	- 3x1 = - 3 u	- 3x2 = - 6 u	- ?
After	5x1 = 5 u	1x2 = 2 u		$174

The amount that Japheth and Jeremy each had at first is the same.  Make the amount that they each had the same.  LCM of 8 and 4 is 8.

Amount that Japheth had more than Jeremy in the end
= 5 u - 2 u
= 3 u

3 u = 42

1 u = 42 ÷ 3 = 14

Amount that Japheth and Jeremy had in the end
= 5 u + 2 u
= 7 u
= 7 x 14
= $98

Amount that Zeph had in the end
= 174 - 98
= $76

Amount that Zeph had at first
= 8 u
= 8 x 14
= $112

Amount that Zeph spent
= 112 - 76
= $36

Answer(s): $36