Zara had $520 less than Valen. Zara spent ¹₇ of her money and Valen spent ³₅ of his money. In the end, Valen and Zara had the same amount of money left. Find the amount of money Valen had at first.

	Zara	Valen	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 Zara's money left
= 1 - ¹₇
= ⁶₇

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

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

⁶₇ of Zara's money = ²₅ of Valen's money
⁶₇ of Zara's money = ⁶₁₅ of Valen's money

Amount that Zara had at first = 7 u
Amount that Valen had at first = 15 u

Amount that Zara had less than Valen had at first
= 15 u - 7 u
= 8 u

8 u = 520

1 u = 520 ÷ 8 = 65

Amount that Valen had at first
= 15 u
= 15 x 65
= $975

Answer(s): $975