Question

The volume of twelve encyclopedias and three dictionaries requires 25.5 inches of space. If five encyclopedias are as thick as three dictionaries, how thick is an encyclopedia and how thick is a dictionary?

Answer 1

Okay, here we have this:

Considering the provided information, we obtain the following system:

`\begin{gathered} \begin{bmatrix}12x+3y=25.5 \\ 5x=3y\end{bmatrix} \\ \end{gathered}`

Now, let's clear x in the first equation:

`\begin{gathered} 12x+3y=25.5 \\ 12x=25.5-3y \\ x=(25.5-3y)/(12) \end{gathered}`

Let's replace in the second equation:

`\begin{bmatrix}5\cdot(25.5-3y)/(12)=3y\end{bmatrix}`

Solving for y:

`\begin{gathered} (102.5-15y)/(12)=3y \\ 127.5-15y=36y \\ 127.5=51y \\ y=(127.5)/(51) \\ y=2.5 \end{gathered}`

Then, x:

`\begin{gathered} x=(25.5-3\cdot2.5)/(12) \\ x=(25.5-7.5)/(12) \\ x=(18)/(12) \\ x=1.5 \end{gathered}`

Finally we obtain that each encyclopedia measures 1.5 inches and each dictionary 2.5 inches.