Xylia had $296 less than Archie. Xylia spent ¹₇ of her money and Archie spent ³₅ of his money. In the end, Archie and Xylia had the same amount of money left. Find the amount of money Archie had at first.

	Xylia	Archie	Difference
Before	7x1 = 7 u	5x3 = 15 u	8 u
Change	- 1x1 = - 1 u	- 3x3 = - 9 u
After	6x1 = 6 u	2x3 = 6 u

Fraction of Xylia's money left
= 1 - ¹₇
= ⁶₇

Fraction of Archie's money left
= 1 - ³₅
= ²₅

Archie and Xylia had the same amount of money in the end. Make the numerators the same. LCM of 6 and 2 is 6.

⁶₇ of Xylia's money = ²₅ of Archie's money
⁶₇ of Xylia's money = ⁶₁₅ of Archie's money

Amount that Xylia had at first = 7 u
Amount that Archie had at first = 15 u

Amount that Xylia had less than Archie had at first
= 15 u - 7 u
= 8 u

8 u = 296

1 u = 296 ÷ 8 = 37

Amount that Archie had at first
= 15 u
= 15 x 37
= $555

Answer(s): $555