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.

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.