on the polarknit yarn website (polarknit brand offers both finished products, and plain yarns) they have a free scarf pattern. the scarves are 4.75 or 6 wide, and both 62 long. they both use 2 balls of the worsted. http://yarn.polarknit.com/wp-content/uploads/2011/03/2-Lacy-Scarves.pdf - your project is about 3-4x that width, so that’d math out to 6-8 balls, but in a lace pattern.
but… it all depends on pattern, needles, and gauge, not just overall finished size. i’d take a look at the project page for the yarn on ravelry, and see what looks closest to what you want. most of those have better yarn estimates.
also, polarknit’s site references vendor locations. if one is near you, it might make sense to buy locally/regionally, and return any extra… just a thought