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

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.