Natalie had $460 less than Elijah. Elijah spent 0.6 of his money and Natalie spent 0.2 of her money. In the end, Elijah and Natalie had the same amount of money left. Find the amount of money Natalie had at first.

	Natalie	Elijah	Difference
Before	5 u	10 u	5 u
Change	- 2 u	- 4 u
After	4 u	4 u

0.6 = ³₅

Fraction of Elijah's amount left
= 1 - ³₅
= ²₅

0.2 = ¹₅

Fraction of Natalie's amount left
= 1 - ¹₅
= ⁴₅

The amount that Elijah and Natalie each had in the end is the same. Make the numerators the same. LCM of 2 and 4 is 4.

²₅ of Elijah's amount = ⁴₅ of Natalie's amount
⁴₁₀ of Elijah's amount = ⁴₅ of Natalie's amount

Amount that Natalie had less than Elijah
= 10 u - 5 u
= 5 u

5 u = 460

1 u = 460 ÷ 5 = 92

Amount that Natalie had at first
= 5 u
= 5 x 92
= $460

Answer(s): $460