Nicole had $686 less than Rael. Nicole spent ¹₇ of her money and Rael spent ⁴₇ of his money. In the end, Rael and Nicole had the same amount of money left. Find the amount of money Rael had at first.

	Nicole	Rael	Difference
Before	7x1 = 7 u	7x2 = 14 u	7 u
Change	- 1x1 = - 1 u	- 4x2 = - 8 u
After	6x1 = 6 u	3x2 = 6 u

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

Fraction of Rael's money left
= 1 - ⁴₇
= ³₇

Rael and Nicole had the same amount of money in the end. Make the numerators the same. LCM of 6 and 3 is 6.

⁶₇ of Nicole's money = ³₇ of Rael's money
⁶₇ of Nicole's money = ⁶₁₄ of Rael's money

Amount that Nicole had at first = 7 u
Amount that Rael had at first = 14 u

Amount that Nicole had less than Rael had at first
= 14 u - 7 u
= 7 u

7 u = 686

1 u = 686 ÷ 7 = 98

Amount that Rael had at first
= 14 u
= 14 x 98
= $1372

Answer(s): $1372