Chapter 3.1, Problem 3LC

Solution

The number of pens and pencils bought.

The person buys $2$ pens and $4$ pencils.

Given information:

Cost of total of $6$ pens and pencils $=\$4$

Cost of each pen $=\$1$

Cost of each pencils $=\$0.50$

Calculation:

Let, Number of pens $=x$

Number of pencils $=y$

Given that, the person buys a total of 6 pens and pencils:

  $x+y=6\to \left(1\right)$

Cost of each pen $=\$1$ and cost of each pencils $=\$0.50$ and the person spends $\$4$ on both pen and pencils.

  $1x+0.5y=4\to \left(2\right)$

Thus, the system o equations are:

  $\left\{\begin{array}{r}\hfill x+y=6\to \left(1\right)\\ \hfill x+0.50y=4\to \left(2\right)\end{array}\right.$

Graph the equations $\left(1\right)$ and $\left(2\right)$:

  

From the graph, it can be seen that the graphs of the equations $x+y=6$ and $x+0.50y=4$ intersects at the points $\left(2,4\right)$ .

Check for the solution:

Substitute $x=2$ and $y=4$ in the equation $x+y=6$ :

  $\begin{array}{c}2+4=6\\ 6=6\end{array}$

Substitute $x=2$ and $y=4$ in the equation $x+0.50y=4$ :

  $\begin{array}{c}2+0.50\left(4\right)=4\\ 2+2=4\end{array}$

The equations are satisfied.

Thus, the person buys, $2$ pens and $4$ pencils.