Esther had $360 less than Howard. Howard spent 0.6 of his money and Esther spent 0.2 of her money. In the end, Howard and Esther had the same amount of money left. Find the amount of money Esther had at first.

	Esther	Howard	Difference
Before	5 u	10 u	5 u
Change	- 2 u	- 4 u
After	4 u	4 u

0.6 = ³₅

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

0.2 = ¹₅

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

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

²₅ of Howard's amount = ⁴₅ of Esther's amount
⁴₁₀ of Howard's amount = ⁴₅ of Esther's amount

Amount that Esther had less than Howard
= 10 u - 5 u
= 5 u

5 u = 360

1 u = 360 ÷ 5 = 72

Amount that Esther had at first
= 5 u
= 5 x 72
= $360

Answer(s): $360