Yen had $2369 less than Riordan. Yen spent ¹₆ of her money and Riordan spent ⁵₇ of his money. In the end, Riordan and Yen had the same amount of money left. Find the amount of money Riordan had at first.

	Yen	Riordan	Difference
Before	6x2 = 12 u	7x5 = 35 u	23 u
Change	- 1x2 = - 2 u	- 5x5 = - 25 u
After	5x2 = 10 u	2x5 = 10 u

Fraction of Yen's money left
= 1 - ¹₆
= ⁵₆

Fraction of Riordan's money left
= 1 - ⁵₇
= ²₇

Riordan and Yen had the same amount of money in the end. Make the numerators the same. LCM of 5 and 2 is 10.

⁵₆ of Yen's money = ²₇ of Riordan's money
¹⁰₁₂ of Yen's money = ¹⁰₃₅ of Riordan's money

Amount that Yen had at first = 12 u
Amount that Riordan had at first = 35 u

Amount that Yen had less than Riordan had at first
= 35 u - 12 u
= 23 u

23 u = 2369

1 u = 2369 ÷ 23 = 103

Amount that Riordan had at first
= 35 u
= 35 x 103
= $3605

Answer(s): $3605