英數~請進~10pts~

Raymond用了身上75分之13的錢去買了一本書,另外又用左餘下31分之21的錢買了一隻錶,最後剩番$120,問原本他有幾多錢?
let y be Raymond's money at first
13y/75 + (y-13y/75)*21/31 + 120 = y
13y/75 + 21y/31 - 13*21y/(75*31) + 120 = y
13*31y/(75*31) + 21*75y/(31*75) - 13*21y/(75*31) = y - 120
(13*31y + 21*75y - 13*21y)/(75*31) = y - 120
y(403 + 1575 - 273) = 75*31*(y - 120)
1705y = 2325y - 279000
279000 = 2325y - 1705y
279000 = 620 y
y = 450
proof:
book = 13y/75 = 13*450/75 = 78
watch = (y-13y/75)*21/31 = (450-78)*21/31 = 372*21/31 = 252
book + watch + on hand = 78 + 252 + 120 = 450

When Raymond spnet 13/75 of his money on a book, then he left (1-13/75) money.
Next, he spent 21/31 of the remainder, then he got (1-21/31) money
finally.

Let the money he had as Y
(Y)(1-13/75)(1-21/31)=120
(Y)(62/75)(10/31)=120
(Y)(62/75)=372
Y=450

OR

(120) / (1-21/31) / (1-13/75)
=450

Ans. He had $450 at first.