Question

Alexia and Olivia are going to the movies. Olivia purchases 2 large popcorns and 4 large sodas for $30.50. Alexia purchases 3 large popcorns and 2 large sodas for $31.75. What is the cost of each item (large popcorn and large soda)?

Answer 1

The cost of one large popcorn is $8.25, and the cost of one large soda is $3.50. We found the prices by creating a system of equations based on the given purchases and solving it using the elimination method.

Step-by-step explanation:

To solve the problem of determining the cost of each item (large popcorn and large soda), we set up two equations based on the given purchases of Alexia and Olivia:

1. Olivia: 2P + 4S = $30.50
2. Alexia: 3P + 2S = $31.75

We can solve this system of equations using either substitution or elimination method. Let's use the elimination method:

1. Multiply the second equation by 2 to match the number of sodas in the first equation: 6P + 4S = $63.50
2. Subtract the first equation from this new equation: (6P + 4S) - (2P + 4S) = ($63.50 - $30.50)
3. Simplify to find the price of popcorn: 4P = $33
4. Divide by 4 to find the price of one large popcorn: P = $8.25
5. Substitute the price of popcorn back into one of the original equations: 2($8.25) + 4S = $30.50
6. Simplify and solve for S: $16.50 + 4S = $30.50, so 4S = $14
7. Divide by 4 to find the price of one large soda: S = $3.50

Therefore, the cost of one large popcorn is $8.25 and the cost of one large soda is $3.50.