Density of an object
You have the right idea, but somewhere your math is incorrect.
Let the mass of the penny be $M$.
The mass of the copper is $\pu{0.03M}$ and the mass of the zinc is $\pu{0.97M}$.
The volume of copper is $\pu{0.03M}/(\pu{8.93g/cm^3})$ and the volume of the zinc is $\pu{0.97M}/(\pu{7.14g/cm^3})$.
The total volume is
$$\pu{0.03M}/(\pu{8.93g/cm^3}) + \pu{0.97M}/(\pu{7.14g/cm^3})$$
The density of the penny is
$$\frac {M}{\pu{0.03M}/(\pu{8.93g/cm^3}) + \pu{0.97M}/(\pu{7.14g/cm^3})}$$
Factoring out M gives
$$\frac {1}{0.03/(\pu{8.93g/cm^3}) + 0.97/(\pu{7.14g/cm^3})}$$
So the density of a mixture works out to be:
$$D=\frac {1}{(\%_1/D_1)+(\%_2/D_2)}$$