Molar Fractions, fucking chemistry

Okay, so an element Q exists in two states, 320Q and 319Q. It's overall atomic mass is 319.58 as it appears on a hypothetical periodic table. 319Q's atomic mass is 319.02 g/mol and 320Q's atomic mass is 320.04 g/mol. The 319.58 is composed of the average amount of the two per mol of Q. What are the molar fractions of 320Q and 319Q respectively?

Me and my friend have been trying to figure this out and he says it's done like this:

%320Q=320.04/(319.02+320.04) to get .5007980471 (5008%)

I say that's bullshit because by just plug 'n checking I get that Q320 should be closer to 55%

How is this type of problem done?

A molar fraction (noted xi) is what % of a given substance is in a mole of your compound (for example if element Q is one-third Q319 and two-thirds Q320 their respective molar fractions are .33 and .66)

From the problem we can write two equations
a) x + y = 1
where x is the molar fraction of Q319 and y the molar fraction of Q320. there are only two substances so their sum must equal 100% (1)

b)319.02*x + 320.04*y = 319.58*1
this is a similar equation but each term has been multiplied by its respective molar mass (noted Mi) I'm probably not explaining this enough but look up in your manual: moles, molar mass, molar fraction. M1 * x1 + M2 * x2 = M3 * (x1+x2)

replace x by 1-y, isolate y
y = 0,549 = 54.9%
x is the remainder (1-0.549) = 0,451 = 45.1%

45.1% Q319, 54.9% Q320

Without banging my head too much what your friend did is probably incorrect because it doesn't take into account the overall molar mass of the substance