Answer :
This problem will lead us to a system of simultaneous equations.
Let x represent hardcover books,
Let y represent paperback books,
Therefore, we have:
[tex]\begin{gathered} x+y=12\ldots(1) \\ 4x+2y=36\ldots(2) \end{gathered}[/tex]We will solve via the elimination method.
[tex]\begin{gathered} \text{ We multiply eqn 1 by 2 and eqn 2 by 1 to get:} \\ 2x+2y=24\ldots(3) \\ 4x+2y=36\ldots(4) \\ \text{ Subtract eqn 3 from 4 to get:} \\ 2x=12 \\ \text{Divide both sides by 2 to get:} \\ x=\frac{12}{2}=6 \end{gathered}[/tex]Having solved for x, we substitute this value of x into equation q to get y as:
[tex]\begin{gathered} 6+y=12 \\ \text{ We subtract 6 from both sides to get:} \\ y=12-6=6 \end{gathered}[/tex]x = 6,
y = 6