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Question

Camden and Aiden went to the movie theater. Camden bought two buckets of popcorn and one box of candy for $15.50. Aiden bought one bucket of popcorn and one box of candy for $12.45. Write a system of equations that can be used to determine p, the cost of one bucket of popcorn, and c, the cost of one box of candy.
Responses

A 2p - c = 15.50

p + c = 12.452 p - c = 15.50 p + c = 12.45

B 2p + c = 15.50

p - c = 12.452 p + c = 15.50 p - c = 12.45

C 2p + c = 15.50

p + c = 12.452 p + c = 15.50 p + c = 12.45

D 2p - c = 15.50

p - c = 12.452 p - c = 15.50 p - c = 12.45

Answer 1

To determine the cost of one bucket of popcorn (p) and one box of candy (c), we need to set up a system of equations based on the purchases made by Camden and Aiden.

From the information provided:

• Camden bought 2 buckets of popcorn and 1 box of candy for $15.50. This can be represented by the equation: \( 2p + c = 15.50 \)

• Aiden bought 1 bucket of popcorn and 1 box of candy for $12.45. This can be represented by the equation: \( p + c = 12.45 \)

Putting these together, the system of equations is:

1. \( 2p + c = 15.50 \)
2. \( p + c = 12.45 \)

Looking at the provided response options, we can determine the correct answer:

The correct system of equations is: A:

• \( 2p + c = 15.50 \)
• \( p + c = 12.45 \)

So the answer is A:

1. \( 2p + c = 15.50 \)
2. \( p + c = 12.45 \)