Elyse had $470 less than Gabriel. Gabriel spent 0.8 of his money and Elyse spent 0.4 of her money. In the end, Gabriel and Elyse had the same amount of money left. Find the amount of money Elyse had at first.

	Elyse	Gabriel	Difference
Before	5 u	15 u	10 u
Change	- 1 u	- 3 u
After	3 u	3 u

0.8 = ⁴₅

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

0.4 = ²₅

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

The amount that Gabriel and Elyse each had in the end is the same. Make the numerators the same. LCM of 1 and 3 is 3.

¹₅ of Gabriel's amount = ³₅ of Elyse's amount
³₁₅ of Gabriel's amount = ³₅ of Elyse's amount

Amount that Elyse had less than Gabriel
= 15 u - 5 u
= 10 u

10 u = 470

1 u = 470 ÷ 10 = 47

Amount that Elyse had at first
= 5 u
= 5 x 47
= $235

Answer(s): $235