Let his total money be x.
He spent (3/7)x of his money.
He gave 1/4(x-3/7x) to his sister.
which is : (1/4)(4/7)x = (1/7)x
Now,
How much money he have in the beginning =
(3/7)x+(1/7)x+120=x
(4/7)x+120=x
120=x-(4/7)x
120=(3/7)x
x=1207/3 [cross multiplication]
x=280.
So, Alex had $280 in the beginning.