= Solution
Let $V_c$ be the carbon-fibre <volume fraction> of the whole composite. Then $V_m=0.4$ and $V_g=0.6-V_c$. Under the same <longitudinal rule of mixtures>,
$$
E=3(0.4)+75(0.6-V_c)+220V_c=46.2+145V_c\quad\mathrm{GPa}.
$$
Setting $E=71.94\,\mathrm{GPa}$ gives
$$
\boxed{V_c=0.1775,\qquad V_g=0.4225,\qquad V_m=0.4000.}
$$
Thus carbon occupies \b[17.8% of the complete composite], or about $29.6\%$ of its total fibre <volume>. The resulting $60\%$ total fibre fraction is much more plausible than the glass-only estimate. This remains an ideal stiffness calculation requiring aligned, effectively loaded fibres; strength and fatigue checks are separate.
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