Home > PC3 > Chapter 9 > Lesson 9.1.4 > Problem9-86

9-86.

Juanita wants to solve the following problem using matrices, but is not sure how.

The cost of two pencils, two pens, and two erasers is $2.46$. The cost of two pencils, five pens, and one eraser is $4.38$. The cost of one pencil, one pen, and two erasers is $1.38$. What is the cost of each item?

1. Explain what she should do.

Think about how you would write an equation for each sentence.
What would your system of equations look like?
$\begin{bmatrix}2&2&2\\2&5&1\\1&1&2\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}2.46\\4.38\\1.38\end{bmatrix}$
$\text{Where }x = \text{cost of } 1 \text{ pencil}, y = \text{cost of } 1 \text{ pen}, z = \text{ cost of } 1 \text{ eraser.}$
Solve for $x, y,$ and $z$ using a calculator.