Roger spent $390 on a toy car. He spent 1/5 of his remaining money on a belt. If he had 3/7 of his money left, how much money did Roger have at first?

started with m

after car had (m - 390)
then spent (m-390)/5 on belt
so has spent 390 + (m-390)/5
that is 1 - 3/7 = (4/7) m is spent
so
(4/7) m = 390 + (m-390)/5
(4/7) m = 312 + m / 5
(4/7 - 1/5) m = 312
(20 -7) m = 312 * 35
m = 312 * 35 / 13
m = 840