Question

Yesterday, a movie theater sold 268 bags of popcorn. A large bag of popcorn costs $4, and a small bag of popcorn costs $1. In all, the movie theater made $505 from popcorn sales. Write and solve a system of equations to find how many bags of each size of popcorn were sold.

a) 3x + y = 268; 4x + y = 505
b) 2x + 3y = 268; 3x + y = 505
c) x + 4y = 268; 2x + 3y = 505
d) 3x + 2y = 268; x + 4y = 505

Answer 1

By setting up a system of equations using the variables x and y to represent the number of large and small bags of popcorn sold, respectively, and solving them, we find that 79 large bags and 189 small bags of popcorn were sold.

Step-by-step explanation:

To solve the problem of determining the number of large and small bags of popcorn sold at the movie theater, we need to set up a system of equations based on the given information. Let x represent the number of large bags of popcorn sold, and y represent the number of small bags of popcorn sold.

We have two pieces of information that can be translated into equations:

• Total bags of popcorn sold: x + y = 268
• Total revenue from popcorn sales: 4x + y = 505
  

Now, let's solve this system of equations.

1. From the first equation (x + y = 268), we can express y in terms of x: y = 268 - x.
2. Substitute the value of y from the first equation into the second equation (4x + y = 505) to get: 4x + (268 - x) = 505, which simplifies to 3x = 237.
3. Dividing both sides by 3 gives us x = 79. This means 79 large bags of popcorn were sold.
4. Substitute x back into the expression for y: y = 268 - 79, which gives us y = 189. So, 189 small bags of popcorn were sold.

The correct system of equations and the number of each size of popcorn bags sold are found after solving the equations.