Calculating the percent composition of weight of an alloy

[shreddinglicks]

Homework Statement

There is an alloy:
ρ=7.64 g/〖cm〗^3
Σ_a=.205 〖cm〗^(-1)
Σ_s=.956〖cm〗^(-1)

It has properties of two elements:
iron
M = 55.84 g/mol
σ_a=2.56 b
σ_s=11.2 b

carbon
M = 12 g/mol
σ_a=.0035 b
σ_s=5.55 b

Find the percent composition by weight of iron and carbon in the alloy.

Relevant Equations

Σ=σN eq 1
N=(ρN_a)/M eq 2

I found the density of carbon and iron:
ρ_fe=7.87 g/〖cm〗^3
ρ_c=2.26 g/〖cm〗^3

Using equation 2:
atom density of iron and carbon

N_fe = 8.48e22 cm^-3
N_c = 1.13e23 cm^-3

Using equation 1:
macroscopic scatter and absorption cross sections of iron and carbon

Σ_a,fe = .217 cm^-1
Σ_s,fe = .949 cm^-1

Σ_a,c = 3.95e-4 cm^-1
Σ_s,c = .627 cm^-1

I'm lost. I think I need to get the gram atomic weight of the alloy and do a ratio:

M_i/M_alloy

to get the weight percent. I need the number density to do that and I don't see a clear way of getting it. Or maybe my approach is completely wrong.

 

[anuttarasammyak]

σ_a=2.56 b
σ_s=11.2 b

I am a layman on metal. Could you tell me what a, s, and b are ?