x - the number of sandwiches ordered
y - the number of soups ordered
There were 18 people, and each person ordered either one soup or one sandwich.
[tex]x+y=18[/tex]
The sandwiches cost $7.75 each, the soups cost $4.50 each. The total cost was $113.50.
[tex]7.75x+4.5y=113.5[/tex]
Set up a system of equations:
[tex]x+y=18 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\times (-4.5) \\
7.75x+4.5y=113.5 \\ \\
-4.5x-4.5y=-81 \\
\underline{7.75x+4.5y=113.5} \\
3.25x=32.5 \\
x=\frac{32.5}{3.25} \\
x=10[/tex]
10 sandwiches were ordered.
The answer is D.
