Risa had $375 less than Riordan. Risa spent ¹₃ of her money and Riordan spent ⁴₇ of his money. In the end, Riordan and Risa had the same amount of money left. Find the amount of money Riordan had at first.

	Risa	Riordan	Difference
Before	3x3 = 9 u	7x2 = 14 u	5 u
Change	- 1x3 = - 3 u	- 4x2 = - 8 u
After	2x3 = 6 u	3x2 = 6 u

Fraction of Risa's money left
= 1 - ¹₃
= ²₃

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

Riordan and Risa had the same amount of money in the end. Make the numerators the same. LCM of 2 and 3 is 6.

²₃ of Risa's money = ³₇ of Riordan's money
⁶₉ of Risa's money = ⁶₁₄ of Riordan's money

Amount that Risa had at first = 9 u
Amount that Riordan had at first = 14 u

Amount that Risa had less than Riordan had at first
= 14 u - 9 u
= 5 u

5 u = 375

1 u = 375 ÷ 5 = 75

Amount that Riordan had at first
= 14 u
= 14 x 75
= $1050

Answer(s): $1050