Mod Numbers/Check digits

[upnorthmath]

I have a few homework problems that deal with mod numbers and story problems involving check digits. Here is one example: The following is the UPC code for blue corn chips. Find the missing digit.
0 15839 (missing number)0001 5

Has anyone ever done one of these? This problem is out of the book: The Heart of Mathematics. I'm not even sure where to begin

 

[galactus]

UPC codes involve mod arithmetic. Many do not realize how they are used. It's rather interesting.

Take the dot product of your UPC number and 3,1,3,1,3,1,3,1,3,1,3,1

\(\displaystyle \text{DotP}([0,1,5,8,3,9,x,0,0,0,1,5][3,1,3,1,3,1,3,1,3,1,3,1])=3x+50\)

The result must be 0 mod 10. That is, 10 must divide evenly into it.

What value of x makes 3x+50 divisible by 10. With x being a digit 0 - 9.