Ivory had $260 less than Perry. Ivory spent ¹₅ of her money and Perry spent ³₅ of his money. In the end, Perry and Ivory had the same amount of money left. Find the amount of money Perry had at first.

	Ivory	Perry	Difference
Before	5x1 = 5 u	5x2 = 10 u	5 u
Change	- 1x1 = - 1 u	- 3x2 = - 6 u
After	4x1 = 4 u	2x2 = 4 u

Fraction of Ivory's money left
= 1 - ¹₅
= ⁴₅

Fraction of Perry's money left
= 1 - ³₅
= ²₅

Perry and Ivory had the same amount of money in the end. Make the numerators the same. LCM of 4 and 2 is 4.

⁴₅ of Ivory's money = ²₅ of Perry's money
⁴₅ of Ivory's money = ⁴₁₀ of Perry's money

Amount that Ivory had at first = 5 u
Amount that Perry had at first = 10 u

Amount that Ivory had less than Perry had at first
= 10 u - 5 u
= 5 u

5 u = 260

1 u = 260 ÷ 5 = 52

Amount that Perry had at first
= 10 u
= 10 x 52
= $520

Answer(s): $520