Kimberly had $420 less than Gabriel. Gabriel spent 0.9 of his money and Kimberly spent 0.3 of her money. In the end, Gabriel and Kimberly had the same amount of money left. Find the amount of money Kimberly had at first.

	Kimberly	Gabriel	Difference
Before	10 u	70 u	60 u
Change	- 1 u	- 7 u
After	7 u	7 u

0.9 = ⁹₁₀

Fraction of Gabriel's amount left
= 1 - ⁹₁₀
= ¹₁₀

0.3 = ³₁₀

Fraction of Kimberly's amount left
= 1 - ³₁₀
= ⁷₁₀

The amount that Gabriel and Kimberly each had in the end is the same. Make the numerators the same. LCM of 1 and 7 is 7.

¹₁₀ of Gabriel's amount = ⁷₁₀ of Kimberly's amount
⁷₇₀ of Gabriel's amount = ⁷₁₀ of Kimberly's amount

Amount that Kimberly had less than Gabriel
= 70 u - 10 u
= 60 u

60 u = 420

1 u = 420 ÷ 60 = 7

Amount that Kimberly had at first
= 10 u
= 10 x 7
= $70

Answer(s): $70