Okay, here we have this:
Considering the provided information, we obtain the following system:
[tex]\begin{gathered} \begin{bmatrix}12x+3y=25.5 \\ 5x=3y\end{bmatrix} \\ \end{gathered}[/tex]Now, let's clear x in the first equation:
[tex]\begin{gathered} 12x+3y=25.5 \\ 12x=25.5-3y \\ x=\frac{25.5-3y}{12} \end{gathered}[/tex]Let's replace in the second equation:
[tex]\begin{bmatrix}5\cdot\frac{25.5-3y}{12}=3y\end{bmatrix}[/tex]Solving for y:
[tex]\begin{gathered} \frac{102.5-15y}{12}=3y \\ 127.5-15y=36y \\ 127.5=51y \\ y=\frac{127.5}{51} \\ y=2.5 \end{gathered}[/tex]Then, x:
[tex]\begin{gathered} x=\frac{25.5-3\cdot2.5}{12} \\ x=\frac{25.5-7.5}{12} \\ x=\frac{18}{12} \\ x=1.5 \end{gathered}[/tex]Finally we obtain that each encyclopedia measures 1.5 inches and each dictionary 2.5 inches.
