Eva had $405 less than Neave. Eva spent ¹₅ of her money and Neave spent ³₅ of his money. In the end, Neave and Eva had the same amount of money left. Find the amount of money Neave had at first.

	Eva	Neave	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 Eva's money left
= 1 - ¹₅
= ⁴₅

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

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

⁴₅ of Eva's money = ²₅ of Neave's money
⁴₅ of Eva's money = ⁴₁₀ of Neave's money

Amount that Eva had at first = 5 u
Amount that Neave had at first = 10 u

Amount that Eva had less than Neave had at first
= 10 u - 5 u
= 5 u

5 u = 405

1 u = 405 ÷ 5 = 81

Amount that Neave had at first
= 10 u
= 10 x 81
= $810

Answer(s): $810