I'm having trouble remembering what type of formula I would use to solve a math problem and how, help please?

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 come $7.75 each and the soups come $4.50 each. If the total cost of all 18 lunches was $113.50, how many sandwiches were ordered? What type of formula would I use and how?I

Answer 1

so let b for sandwitches and s for soups

then will be b+s=18 (1)  and 7.75b+4.5s = 113.50   from the (1) we have b=18-s replace this price to (2)

we get 7.75(18-s)+4.5s=113.5    139.5-7.75s+4.5s=113.5  -3.25s=113.5-139.5   -3.25s=-26   s=-26/-3.25

s=8    so soups = 8 and sandwitches =10