On Sunday they sold twice as many books in-store as the 37 books on Saturday so they sold 2*37 = <<2*37=74>>74
They sold 128 books online on Saturday and increased that number by 34 books on Sunday for a total of 128+34 = <<128+34=162>>162
Over the weekend they sold 37+128+74+162 = <<37+128+74+162=401>>401 books
They started off with 743 books and sold 401 books which brings the inventory to 743-401 = <<743-401=342>>342 books
They have 342 books and received a shipment for 160 bringing their inventory to 342+160 = <<342+160=502>>502 books
#### 502