Chemistry/ Algebra Problem been wracking my brains.

An organic liquid is a mixture of methyl alcohol (CH2OH) and ethyl alcohol (C2H5OH). A 0.220g-sample of the liquid is burned in an excess of O2(g) and yields 0.362g CO2(g) (carbon dioxide).

Set up two algebraic equations, one expressing the mass of carbon dioxide produced in terms of each reagent and the other expressing the mass of sample burned in terms of each reagent.
What is the mass of methyl alcohol (CH3OH) in the sample?

Let x be the mass of CH3OH, then 0.220-x is the mass of C2H5OH. The moles of CH3OH is x/32 and the moles of C2H5OH is (0.220-x)/46. The moles of CO2 is 0.00823 mol.

Solve the problem by considering only the moles of carbon. The moles of carbon atoms on the left must equal the moles of carbon on the right.
moles of carbon in CH3OH = x/32
moles of carbon in C2H5OH = 2(0.220-x)/46 .... since there are two moles of C in ethanol.
moles of carbon in CO2 = 0.00823
Write an equation:
x/32 + (0.440-2x)/46 = 0.00823
solve for x
x = 0.109 g = mass of CH3OH
0.220-x = 0.111 g = mass of C2H5OH