How much did Aaron start with?

Question

Aaron spent 3/7 of his money. He gave 1/4 of the remainder to his sister. He had $120 left. How much money did he have in the beginning? Explain how you got your answer.

Answer 1

(3/7)x + (1/4 * 4/7x) + 120 = x

(3/7)x + (1/7)x + 120 = x

4/7x + 120 = x

120 = (3/7)x

120 / (3/7) = x

120 * (7/3) = x

840/3 = x

280 = x

Answer 2

Assume Aaron had x dollars
he gave 3/7 x away, so he has 4x/7 left.
he gives 1/4 of what he has left to his sister, so he has (3/4)(4x/7) left
(3/4)(4x/7) = 120
12x/28 = 120
x = 120(28/12) = $ 280

Answer 3

280