Abi had $115 less than Rael. Abi spent ¹₄ of her money and Rael spent ²₃ of his money. In the end, Rael and Abi had the same amount of money left. Find the amount of money Rael had at first.

	Abi	Rael	Difference
Before	4x1 = 4 u	3x3 = 9 u	5 u
Change	- 1x1 = - 1 u	- 2x3 = - 6 u
After	3x1 = 3 u	1x3 = 3 u

Fraction of Abi's money left
= 1 - ¹₄
= ³₄

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

Rael and Abi had the same amount of money in the end. Make the numerators the same. LCM of 3 and 1 is 3.

³₄ of Abi's money = ¹₃ of Rael's money
³₄ of Abi's money = ³₉ of Rael's money

Amount that Abi had at first = 4 u
Amount that Rael had at first = 9 u

Amount that Abi had less than Rael had at first
= 9 u - 4 u
= 5 u

5 u = 115

1 u = 115 ÷ 5 = 23

Amount that Rael had at first
= 9 u
= 9 x 23
= $207

Answer(s): $207