Question

One Friday night, a group of friends bought 5 containers of popcorn and 4 granola bars at the movie theatre for $42.50. The next week, the same group of friends bought 3 containers of popcorn and 6 granola bars for $34.50. Let p represent the cost of one container of popcorn. Let g represent the cost of one granola bar. Which system of equations will solve for p and g?
5 p + 4 g = 34.50. 3 p + 6 g = 42.50.
4 p + 5 g = 34.50. 3 p + 6 g = 42.50.
4 p + 5 g = 42.50. 6 p + 3 g = 34.50.
5 p + 4 g = 42.50. 3 p + 6 g = 34.50.

Answer 1

To set up the system of equations based on the information provided:

1. The first purchase consisted of 5 containers of popcorn and 4 granola bars for a total of $42.50. This can be represented as:
\[
5p + 4g = 42.50
\]

2. The second purchase was for 3 containers of popcorn and 6 granola bars for a total of $34.50. This is expressed as:
\[
3p + 6g = 34.50
\]

Therefore, the correct system of equations is:
\[
\begin{align*}
1) & \quad 5p + 4g = 42.50 \\
2) & \quad 3p + 6g = 34.50
\end{align*}
\]

This matches the option:
**5 p + 4 g = 42.50. 3 p + 6 g = 34.50.**