Chapter 6.4, Problem 6P

Solve each word problem

You are getting ready to move and have asked some friends to help. For lunch, you buy the following sandwiches at the local deli for $30: six tuna sandwiches and six turkey sandwiches. Later at night, everyone is hungry again and you buy four tuna sandwiches and eight turkey sandwiches for $30.60. What is the price of each sandwich?

To determine

To determine the price of each sandwich.

Answer to Problem 6P

Price of each sandwich is $2.65

Explanation of Solution

Given information :

Price of six tuna sandwiches and six turkey sandwiches is $30.

Price of four tuna sandwiches and eight turkey sandwiches is $30.6.

Let the price of tuna sandwiches be x and turkey sandwiches be y .

Hence the equation becomes,

  $\begin{array}{l}6x+6y=30\\ 4x+8y=30.6\end{array}$

We shall multiply first equation with 2 and second equation with 3 and then subtract second equation from first. We get,

  $\begin{array}{c}\left(3\left(4x+8y\right)-2\left(6x+6y\right)\right)=3\left(30.6\right)-2\left(30\right)\\ 12x+24y-12x-12y=91.8-60\\ 12y=31.8\\ y=2.65\end{array}$

Hence price of each sandwich is $2.65