Question

​Yesterday, a movie theater sold 290 bags of popcorn. A large bag of popcorn costs ​$4. A small bag of popcorn costs ​$1. In​ all, the movie theater made ​$566 from popcorn sales. Write and solve a system of equations to find how many bags of each size of popcorn were sold.

PLEASE HELP

Answer 1

Explanation:

Let's call the number of large bags of popcorn sold "L" and the number of small bags of popcorn sold "S".

We can set up two equations based on the information given:

L + S = 290 (the total number of bags of popcorn sold)

4L + S = 566 (the total revenue from popcorn sales)

We can use substitution or elimination to solve for L and S.

Substitution:

From the first equation, we know that S = 290 - L. We can substitute this into the second equation:

4L + (290 - L) = 566

Simplifying, we get:

3L + 290 = 566

3L = 276

L = 92

Then we can use the first equation to find S:

L + S = 290

92 + S = 290

S = 198

So the movie theater sold 92 large bags of popcorn and 198 small bags of popcorn.

Elimination:

We can eliminate one variable by multiplying one of the equations by a constant to make the coefficients of one of the variables equal but with opposite signs.

In this case, we can multiply the first equation by 4 to make the coefficients of S equal but with opposite signs:

4L + 4S = 1160

4L + S = 566

Subtracting the second equation from the first, we eliminate L:

3S = 594

S = 198

Then we can use either of the original equations to find L:

L + S = 290

L + 198 = 290

L = 92

So the movie theater sold 92 large bags of popcorn and 198 small bags of popcorn.