Question

Multiple Representations  A group of 3 friends went to the movies. In addition to their​ tickets, they bought a large bag of popcorn to share for ​$6.75. The total was ​$29.25. Write and solve an equation to find the cost of one movie​ ticket, m. Use pencil and paper. Draw a picture to model the equation.
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Part 1
Write an equation that represents the cost of one movie ticket. Choose the correct answer below.
A.
6.75minus3mequals29.25
B.
3mplus6.75equals29.25
C.
3minus6.75mequals29.25
D.
6.75mplus3equals29.25

Answer 1

To find the cost of one movie ticket \( m \), we can set up the equation based on the information provided. The friends bought 3 tickets and one bag of popcorn, and the total cost was \( 29.25 \). Therefore, the correct equation is:

\[ 3m + 6.75 = 29.25 \]

So the correct answer is:

**B. \( 3m + 6.75 = 29.25 \)**

### Solving the Equation

1. **Subtract 6.75 from both sides**:

\[
3m + 6.75 - 6.75 = 29.25 - 6.75
\]

This simplifies to:

\[
3m = 22.50
\]

2. **Divide both sides by 3** to find \( m \):

\[
m = \frac{22.50}{3}
\]

Calculating this gives:

\[
m = 7.50
\]

### Cost of One Movie Ticket
The cost of one movie ticket is \( \boxed{7.50} \).

### Drawing a Picture to Model the Equation
You can visualize this scenario by drawing:

- Three circles (representing the three movie tickets) labeled with \( m \) (the cost of one ticket).
- Next to the circles, you can draw a rectangle, labeled \( 6.75 \) to represent the bag of popcorn.
- Finally, you can label the total area as \( 29.25 \).

Here’s a simple representation in text format:

```
[m] [m] [m] Popcorn
| | | [6.75]
|______|______| ___________
3m Total: 29.25
```

This gives a clear visual representation of the ticket costs and the popcorn cost contributing to the total expense.