Question

Students are buying books for the new semester. Eddie buys the environmental statics book and the set theory book for \( $178$. Leah, who is buying books for her-self and her friend, spends \)localid="1668166077473" $319$on two environmental statistics books, one set theory book, and one educational psychology book. Mehmet buys the educational psychology book and the set theory book for $localid="1668166139019" $147$ in total. How much does each book cost.

Short answer

The cost of the environmental statistics book is$86$ , cost of set theory book is $\$92$and the cost of educational psychology book is$\$55$ .

Step-by-step solution

Given data

Combined cost of the environmental statics book and the set theory book is$\$178$ .

Combined cost of her book and her friend book is$\$319$ .

Combined cost of the educational psychology book and the set theory book is $\$147$.

Calculation of the cost of each book.

Let us assume that the price of the environmental statics book is , price of the set theory book is and the price of the psychology book is$p$ .

It is given that the combined cost of the environmental statics book and the set theory book is$\$178$ .

$e+s=178$

Combined cost of her book and her friend book is$\$319$ .

$2e+s+p=319$

Combined cost of the educational psychology book and the set theory book is$\$147$ .

$s+p=147$

Now make a row matrix with columns $e$,$s$ and$p$ respectively.

$\left[\begin{array}{cccc}1& 1& 0& 178\\ 2& 1& 1& 319\\ 0& 1& 1& 147\end{array}\right]$

Use operation $R_2\to R_2-2R_1$

$\left[\begin{array}{cccc}1& 1& 0& 178\\ 0& -1& 1& -37\\ 0& 1& 1& 147\end{array}\right]$

Use operation, $R_1\to R_1+R_2$, $R_2\to -R_2$ and $R_3\to R_3+R_2$

$\left[\begin{array}{cccc}1& 0& 1& 141\\ 0& 1& -1& 37\\ 0& 0& 2& 110\end{array}\right]$

Use operation $R_3\to \frac{R_3}{2}$

$\left[\begin{array}{cccc}1& 0& 1& 141\\ 0& 1& -1& 37\\ 0& 0& 1& 55\end{array}\right]$

Use operation $R_1\to R_1-R_3$and $R_2\to R_2+R_3$

$\left[\begin{array}{cccc}1& 0& 0& 86\\ 0& 1& 0& 92\\ 0& 0& 1& 55\end{array}\right]$

From the above matrix we can conclude that

$$\begin{gathered} e=\$86 \\ s=\$92 \\ p=\$55 \end{gathered}$$

Therefore the cost of the environmental statistics book is$\$86$ , cost of set theory book is$\$92$ and the cost of educational psychology book is $\$55$.