Question

Students are buying books for the new semester. Brigitte buys the German grammar book and the German novel, Die Leiden des jungen Werther, for$\mathit{Є}\mathbf{64}$ in total. Claude spends$\mathit{Є}\mathbf{98}$ on the linear algebra text and the German grammar book, while Denise buys the linear algebra text and Werther, for $\mathit{Є}\mathbf{76}$. How much does each of the three books cost?

Short answer

The German grammar book, the German novel – Die Leiden des Jungen Werther and the linear algebra text cost, $Є43,Є21$and$Є55$respectively.

Step-by-step solution

Represent the money spent by Brigitte, Claude, and Denise in terms of a system of equations.

The cost of each book can be found using the augmented matrix.

The system of equations is,

$\left|\begin{array}{c}G+W=64\\ G+L=98\\ W+L=76\end{array}\right|$

Represent the above equations in terms of a matrix.

$\left|\begin{array}{cccc}1& 1& 0& 64\\ 1& 0& 1& 98\\ 0& 1& 1& 76\end{array}\right|$

Perform the row operations on the matrix. 

Consider the obtained matrix and reduce it into row echelon form:

$\mathbf{rref}\left|\begin{array}{cccc}1& 1& 0& 64\\ 1& 0& 1& 98\\ 0& 1& 1& 76\end{array}\right|\approx \left|\begin{array}{cccc}1& 0& 0& 43\\ 0& 1& 0& 21\\ 0& 0& 1& 55\end{array}\right|$

The values are, $G=Є43,W=Є21,L=Є55$.

Hence, the German grammar book, the German novel – Die Leiden des Jungen Werther and the linear algebra text cost, $Є43,Є21$and $Є55$respectively.