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ollegr [7]
2 years ago
13

A group of 18 people ordered soup and sandwiches for lunch. Each person in the group had either one soup or one sandwich. The sa

ndwiches 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
Mathematics
1 answer:
sergeinik [125]2 years ago
4 0
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.
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