Question

equation to describe the situation below, solve using elimination, and fill in the blanks. Today's cafeteria specials at a high school in Newport are a deluxe turkey sandwich and a chef salad. During early lunch, the cafeteria sold 63 turkey sandwiches and 29 chef salads, for a total of $368. During the late lunch, 63 turkey sandwiches and 73 chef salads were sold, for a total of $544. How much does each item cost? A turkey sandwich costs $ and a chef salad costs $4 Submit

Answer 1

write the system of equations

$\mleft\{\begin{aligned}63x+29y=368 \\ 63x+73y=544\end{aligned}\mright.$

multiply the second equation by -1 and add it to the first one

$\mleft\{\begin{aligned}63x+29y=368 \\ -63x-73y=-544\end{aligned}\mright.$

add them together

$\begin{gathered} (63-63)x+(29-73)y=-176 \\ -44y=-176 \\ y=\frac{-176}{-44} \\ y=4 \end{gathered}$

after having the value of y, replace it on one of the equations to find the value of x

$\begin{gathered} 63x+29(4)=368 \\ 63x+116=368 \\ 63x=368-116 \\ x=\frac{252}{63} \\ x=4 \end{gathered}$