At first, Ahmad, Ivan and Archie had the same amount of money. After Archie spent some of his money, Ahmad spent ³₇ of his money and Ivan spent ²₃ of his money, Ahmad had $75 more than Ivan. In the end, the total amount of money the three boys had left was $428. How much money did Archie spend?

	Ahmad	Ivan	Archie	Total
Before	7x3 =  21 u	3x7 = 21 u	21 u
Change	- 3x3 = - 9 u	- 2x7 = - 14 u	- ?
After	4x3 = 12 u	1x7 = 7 u		$428

The amount that Ahmad and Ivan 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 Ahmad had more than Ivan in the end
= 12 u - 7 u
= 5 u

5 u = 75

1 u = 75 ÷ 5 = 15

Amount that Ahmad and Ivan had in the end
= 12 u + 7 u
= 19 u
= 19 x 15
= $285

Amount that Archie had in the end
= 428 - 285
= $143

Amount that Archie had at first
= 21 u
= 21 x 15
= $315

Amount that Archie spent
= 315 - 143
= $172

Answer(s): $172