In a Material Science laboratory, a new steel alloy was developed having a thermal neutron absorption macroscopic cross section of 0.2052 cm-1 and scattering macroscopic cross section of 0.9565 cm-1. The density of the alloy, made from iron and carbon, is 7.64 g/cm3. With the properties of the component elements shown below, calculate the percent composition by weight of the iron and carbon in the alloy.

Element Iron Carbon Gram Atomic Weight 55.845 12.011 Ca (barns 2.56 0.0035 0s (barns) 11.22 5.55