Agroup of 18 people ordered soup and sandwiches for lunch. each person in the group had either one soup or one sandwich. e 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?

So if the sandwiches cost $7.75 each and the total was $113.50 that would mean that there were 14 sandwiches bought. So 14 times 7.75 is 108.50. 

4.5(18-y)+7.75y=113.5
My justification fir wirting the equation like this is beacuse the total equals how many people ate over all minus how many people ate the soup. (X=18-y) y=soup x=sandwiches
81-4.5y+7.75y=113.5
We distributed
Now its time to combine like terms.
3.25y+81=113.5
I only subtracted beacuse the 4.5 was negative
Subtract 81 from both sides
3.25y=32.5
Divide by 3.25 on both sides
Y=10
Now that we have that we insert it back into the equation
x=18-(10)
So x=8
Basically, 8 sandwiches were ordered :D