Irene had $500 less than Oliver. Irene spent ¹₄ of her money and Oliver spent ²₃ of his money. In the end, Oliver and Irene had the same amount of money left. Find the amount of money Oliver had at first.

	Irene	Oliver	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 Irene's money left
= 1 - ¹₄
= ³₄

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

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

³₄ of Irene's money = ¹₃ of Oliver's money
³₄ of Irene's money = ³₉ of Oliver's money

Amount that Irene had at first = 4 u
Amount that Oliver had at first = 9 u

Amount that Irene had less than Oliver had at first
= 9 u - 4 u
= 5 u

5 u = 500

1 u = 500 ÷ 5 = 100

Amount that Oliver had at first
= 9 u
= 9 x 100
= $900

Answer(s): $900