(Solved): Part 2: Applications of Modular Arithmetic Barcodes on products were introduced in 1973. The barcod ...

Part 2: Applications of Modular Arithmetic Barcodes on products were introduced in 1973. The barcodes are machine readable versions ofthe UPC (Universal Product Code). The UPC consist of a 6-digit company code, a 5-digit product code and 1 check digit. To determine the correct check digit: 1. Add the digits in odd positions and multiply the total by 3 . 2. Add the digits in even positions. 3. Add the results from steps 1 and 2. 4. The total in step 3 must be equivalent to $0\mathrm{mod}10$, which is another way of saying thatthe result is divisible by 10 . The first 11 digits of the UPC for McCormick's Sea Salt Grinder are 05210002359 . What isthe correct missing check digit? 1) Odd positions: $0+2+0+0+3+9=14?14?3=42$ 2) Even positions: $5+1+0+2+5+x=13+x$ 3) $42+13+x=55+x?0\mathrm{mod}10$