Question

Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.This morning, Mike processed two catering orders at the sandwich shop where he works. The first order was for 1 tray of club sandwiches, at a cost of $9. The second order, which cost $69, was for 5 trays of club sandwiches and 4 trays of vegetarian sandwiches. How much do the trays cost?A tray of club sandwiches costs $? and a tray of vegetarian sandwiches costs $?

Answer 1

`\begin{gathered} \text{ A tray of club sandwiches cost \$9} \\ A\text{ tray of vegetarian sandwiches cost \$6.} \end{gathered}`

Explanation:

Given the information, create the following augmented matrix:

The first order was for 1 tray of club sandwiches, at a cost of $9. The second-order, which cost $69, was for 5 trays of club sandwiches and 4 trays of vegetarian sandwiches.

`\begin{gathered} 5x+4y=69 \\ x=9 \end{gathered}`

Into an augmented matrix:

`\begin{bmatrix}{5} & {4} \\ {\placeholder{⬚}} & {1}\end{bmatrix}\begin{bmatrix}{69} & {} \\ {9} & {}\end{bmatrix}`

Solve.

Let x be the cost of a tray of club sandwiches.

Let y be the cost of a tray of vegetarian sandwiches.

`\begin{gathered} x=9 \\ Substitute\text{ on the first equation} \\ 5(9)+4y=69 \\ 4y=69-45 \\ y=(24)/(4) \\ y=6 \end{gathered}`