Question

Write a system of equations to describe the situation below solve using illumination and fill in the blanks

Answer 1

Let the cost of a tray of club sandwiches be s, and the cost of a tray of vegetarian sandwiches be v.

Then, the first order was for 6 trays of club sandwiches and 3 trays of vegetarian sandwiches at a cost of $75. We have;

`6s+3v=75\ldots\ldots.\ldots\ldots.\text{equation}1`

Also, the second order was for 9 trays of club sandwiches and 9 trays of vegetarian sandwiches at a cost of $144. We have;

`9s+9v=144\ldots.\ldots\ldots\ldots....\ldots\text{equation}2`

We would solve the two equation simultaneously, using elimination method.

Multiply equation 1 by 9 and equation 2 by 3.

`\begin{gathered} (6s+3v=75)*9 \\ 54s+27v=675\ldots.\ldots..\ldots..equation4 \\ (9s+9v=144)*3 \\ 27s+27v=432\ldots\ldots..\ldots equation5 \end{gathered}`

Subtract equation 5 from equation 4. We have;

`\begin{gathered} 54s-27s+27v-27v=675-432 \\ 27s=241 \\ s=(243)/(27) \\ s=9 \end{gathered}`

Substitute the value of s in equation 1. We have;

`\begin{gathered} 6s+3v=75 \\ 6(9)+3v=75 \\ 54+3v=75 \\ \text{Subtract 54 from both sides;} \\ 54-54+3v=75-54 \\ 3v=21 \\ \text{Divide both sides by 3;} \\ (3v)/(3)=(21)/(3) \\ v=7 \end{gathered}`

Thus;

FINAL ANSWER: A tray of club sandwiches costs $9, and a tray of vegetarian sandwiches costs $7