[tex]\{a,b,c\}i.p.\{2,3,4\}\Rightarrow \frac{a}{\frac{1}{2}}=\frac{b}{\frac{1}{3}}=\frac{c}{\frac{1}{4}}=k\Rightarrow a=\frac{k}{2}, b=\frac{k}{3}, c=\frac{k}{4}\\
6a+9b-4c=75\\
6\cdot\frac{k}{2}+9\cdot\frac{k}{3}-4\cdot \frac{k}{4}=75\\
3k+3k-k=75\\
5k=75\Rightarrow \boxed{k=15}\\
a=\frac{k}{2}\Rightarrow \boxed{a=\frac{15}{2}}\\
b=\frac{k}{3}\Rightarrow \boxed{b=5}\\
c=\frac{k}{4}\Rightarrow \boxed{c=\frac{15}{4}}[/tex]
