Chapter 8.3, Problem 81STP

To determine

To Find: The cost of each item on her order is using augmented matrices.

Answer to Problem 81STP

Cost of batteries is $\$74$

Cost of spark plugs $\$58$

Cost of wiper blades $\$48$

Explanation of Solution

Given: Shandra is inventory manager for a local repair shop. She ordered $6$ batteries, $5$ cases of spark plugs, and two dozen pair of wiper blades and pays $\$830$ .She ordered $3$ batteries, $7$ cases of spark plugs, and four dozen pair of wiper blades and pays $\$820$ .

The augmented matrix representing the situation is

  $\left[\begin{array}{ccc}6& 5& 2\\ 3& 7& 4\\ 1& 0& -2\end{array}\right]\begin{array}{c}830\\ 820\\ -22\end{array}$

Now

Using the graphing calculator to solve the system

KEYSTROKES:

  $\begin{array}{l}\text{ENTER}3\\ \text{ENTER}4\\ \text{ENTER}6\\ \text{ENTER}5\\ \text{ENTER}2\\ \text{ENTER}830\\ \text{ENTER}3\\ \text{ENTER}7\\ \text{ENTER}4\\ \text{ENTER}820\\ \text{ENTER}1\\ \text{ENTER}0\\ \text{ENTER}-2\\ \text{ENTER}-22\\ \text{ENTER}\end{array}$

Now

The matrix is

  

Thus

Cost of batteries is $\$74$

Cost of spark plugs $\$58$

Cost of wiper blades $\$48$