Mass Spectrometry Question

In my organic chemistry textbook, there is a question regarding MS and chemical formula determination. The chemical in the question is nicotine, a diamino compound with two rings and a M+=162.1157

the formula has 2 nitrogens (MW 14.0067) for a total of 28.0134 g/m

the rest of the formula is pretty easy to determine, given that there are two rings and no atoms other than N's H's and C's. My method (working out possibilities and rulling them out by the degrees of unsat and such) yielded the right formula (C10 H14 N2)

The solutions guide uses a different method. They subtract the weight of N from the total weight, and then divide the portion of the number (the xxx in abcd.xxxxx, ie the 442 in 18232.442) past the decimal by .00783 (from hydrogen). This yields 14, the number of hydrogens.

What I don't understand is why this works - if carbon had a weight of exacly 12, it would be fine, but unless you are using an isotopically pure source of carbon the weight of carbon, on average, will be the number listed on the periodic table. The number to the right of the decimal is actually larger than the .00783, and I would expect that to confound this calculation beyond repair. What am I missing?