. 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?

Mathematics · College · Tue Nov 03 2020

llm

Answered on Thu Mar 31 2022

Let the number of soup be x

and,number of sandwiches be y
According to question,

x+y= 18 …..(1)

x= 18-y …..(2)

And,

4.50x+7.75y= 113.50 ….(3)

Now, putting value of x in equation 3

4.50(18-y)+7.75y= 113.50

81-4.50y+7.75y= 113.50

3.25y = 113.50 - 81

3.25y = 32.5

y = 32.5/3.25

y = 10

Now, putting value of y in equation (2)

x = 18 - 10

x = 8

Hence, number of sandwiches ordered were 10.