Question

Sterday, a movie theater sold 262 bags of popcorn. a large bag of popcorn costs ​$3. a small bag of popcorn costs ​$1. in​ all, the movie theater made ​$412 from popcorn sales. write and solve a system of equations to find how many bags of each size of popcorn were sold.

Answer 1

They sold 187 small bags and 75 large bags.

Two variables L and S (large & small)

We know that L + S = 262  -> the amount of bags sold

We also know that 3L + 1S = $412 -> total money made

L = 262 - S 

Plug that into the second equation:

3(262 - S) + 1S = 412

786 - 3S + 1S = 412

786 - 2S = 412
786 - 412 = 2S
374 = 2S
S = 187
187 small bass and 
So they sold 187 small bags

L = 262 - 187 = 75 

They sold 75 large bags.