How do I calculate the % abundances of two copper isotopes given the mass of each isotope and the molar mass?

Question

Copper metal is a mixture of two isotopes:

Cu-63 mass = 62.9298 u, and Cu-65 mass 64.9278 u

Molar mass of Cu: 64.546 g/mole

Calculate % abundances of the two isotopes.

Can someone explain how to go about doing this?

Answer 1

Let x = % abundance of Cu-63 and let y = % abundance of Cu-65

x + y = 100

64.546 = 62.9298 x + 64.9278 ( 100-x) / 100

64.546 = 62.9298 x + 6492.78 - 64.0278 x / 100

6454.6 = - 1.098 x + 6492.78

38.18 = 1.098 x

x = 34.8 % => Cu-63