Archie, Albert and Valen shared $455. During a shopping trip, Archie spent ²₉ of his share, Albert spent ³₇ of his share and Valen spent ¹₄ of his share. Given that all three boys each spent the same amount of money, how much more money do Archie and Albert have than Valen at first?

	Archie	Albert	Valen	Total
Before	9x3 = 27 u	7x2 = 14 u	4x6 = 24 u	$455
Change	- 2x3 = - 6 u	- 3x2 = - 6 u	- 1x6 = - 6 u
After	7x3 = 21 u	4x2 = 8 u	3x6 = 18 u

The amounts that Archie, Albert and Valen spent is the same.  Make the amounts that each boy spent the same. LCM of 2, 3 and 1 is 6.

Amounts that the 3 boys had at first
= 27 u + 14 u + 24 u
= 65 u

65 u = 455

1 u = 455 ÷ 65 = 7

Amount that Archie and Albert have at first
= 27 u + 14 u
= 41 u

Amount that Archie and Albert have more than Valen at first
= 41 u - 24 u
= 17 u
= 17 x 7
= $119

Answer(s): $119