Ashop owner sold 175 shirts. he donated 1/9 of the remaining shirts to charity and had 4/7 of the shirts left. how many shirts did he have at first?

I think the answer is 490 shirts, right???
because
firstly, let X be the total shirts you need to find
then we have 175/X is the rate of shirts which the shop owner sold in the begining
so the remaining rate is (1-175/X)
the shop owner sold again and the second rate which shows the shirts was donated to the charity is (1-175/X)x1/9
so the overall rate that shows the owner shop sold in 2 turns is 175/X+(1-175/X)x1/9
that rate below is also 1-4/7 or 3/7
so solves 175/X+(1-175/X)x1/9=3/7<=>X=490