Agroup 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

Let a be the number of soups ordered and b be the number of sandwiches ordered. We know that, a + b = 18, so a = 18 - b. Now we form an equation for the total cost, which is: 4.5a + 7.75b = 113.5. Now, we substitute the value of a into the cost equation to form a single equation in terms of b, number of sandwiches, only. 4.5(18 - b) + 7.75b = 113.5. Solving for b, we get b = 10. Therefore, the answer is D.