We have the following relationships from the question:
[tex]\begin{gathered} 24-karat\Rightarrow100\% \\ x-karat\Rightarrow75\% \\ 12-karat\Rightarrow50\% \end{gathered}[/tex]Therefore, we can have the following equation to solve the problem:
[tex]\frac{24-x}{100-75}=\frac{24-12}{100-50}[/tex]We can solve the equation as follows:
[tex]\begin{gathered} \frac{24-x}{25}=\frac{12}{50} \\ 24-x=\frac{12\times25}{50} \\ 24-x=6 \\ \therefore \\ x=24-6 \\ x=18 \end{gathered}[/tex]Therefore, 18-karat gold is 75% gold.
