Question

A group of 18 people ordered soup and sandwiches for lunch. Each person in the group had either one soup or one sandwich. The sandwiches cost $7.75 each
and the soups cost $4.50 each. If the total cost of all 18 lunches was $113.50, how many sandwiches were ordered?

A. 7

B. 8

C. 9

D. 10

Answer 1

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.
$x+y=18$

The sandwiches cost $7.75 each, the soups cost $4.50 each. The total cost was $113.50.
$7.75x+4.5y=113.5$

Set up a system of equations:
$x+y=18 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\times (-4.5) \\ 7.75x+4.5y=113.5 \\ \\ -4.5x-4.5y=-81 \\ \underline{7.75x+4.5y=113.5} \\ 3.25x=32.5 \\ x=\frac{32.5}{3.25} \\ x=10$

10 sandwiches were ordered.
The answer is D.