Chapter 9.3, Problem 14P

To determine

To find: The cost of each pen and the pencil.

Answer to Problem 14P

The cost of pen is $\$1.25$ and the cost of mechanical pencil is $\$1.50$ .

Explanation of Solution

Given:

Thechange received from payment of $\$10$ bill on buying six pens and one mechanical pencil is $\$1$ .

The change is $\$2$ when four pens and two mechanical pencils are bought.

Calculation:

Consider the number of pen is $p$ and the number of mechanical pencil is $m$ .

Consider the change received from payment of $\$10$ bill on buying six pens and one mechanical pencil is $\$1$ , then the change equation for the condition is,

  $\begin{array}{l}6p+m=10-1\\ 6p+m=9\end{array}$

Consider change received is $\$2$ when four pens and two mechanical pencils are bought.

  $\begin{array}{l}4p+2m=10-2\\ 4p+2m=8\\ 2p+m=4\end{array}$

Subtract the first equation from second as,

  $\begin{array}{l}6p+m-2p-m=9-4\\ 4p=5\\ p=\$1.25\end{array}$

Then, the cost of the pencil is,

  $\begin{array}{l}2\left(1.25\right)+m=4\\ m=\$1.50\end{array}$