Question
Multiple Representations A group of 4 friends went to the movies. In addition to their tickets, they bought a large bag of popcorn to share for $7.25. The total was $45.25. 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.
Question content area bottom
Part 1
Write an equation that represents the cost of one movie ticket. Choose the correct answer below.
A.
7.25mplus4equals45.25
B.
7.25minus4mequals45.25
C.
4minus7.25mequals45.25
D.
4mplus7.25equals45.25
Question content area bottom
Part 1
Write an equation that represents the cost of one movie ticket. Choose the correct answer below.
A.
7.25mplus4equals45.25
B.
7.25minus4mequals45.25
C.
4minus7.25mequals45.25
D.
4mplus7.25equals45.25
Answers
GPT-4o mini
To solve for the cost of one movie ticket (m), we need to consider that there are 4 friends who each buy one movie ticket, in addition to sharing a large bag of popcorn that costs $7.25. The total cost for the tickets and popcorn adds up to $45.25.
The correct representation of this scenario can be expressed in the following way:
1. The total cost of the tickets for 4 friends is \(4m\) (where \(m\) represents the cost of one ticket).
2. We add the cost of the popcorn ($7.25) to that total.
3. The equation to represent this situation is:
\[ 4m + 7.25 = 45.25 \]
Thus, the correct answer is:
**D. \(4m + 7.25 = 45.25\)**
Now we can solve for \(m\):
1. Subtract 7.25 from both sides:
\[
4m + 7.25 - 7.25 = 45.25 - 7.25
\]
\[
4m = 38.00
\]
2. Divide both sides by 4:
\[
m = \frac{38.00}{4} = 9.50
\]
So, the cost of one movie ticket is **$9.50**.
### Drawing a Picture to Model the Equation
You can visualize this equation as follows:
```
+--------------------+
| |
| Popcorn | $7.25
| |
+--------------------+
+------------------+ +------------------+ +------------------+ +------------------+
| | | | | | | |
| Movie Ticket 1| | Movie Ticket 2| | Movie Ticket 3| | Movie Ticket 4|
| (m) | | (m) | | (m) | | (m) |
| | | | | | | |
+------------------+ +------------------+ +------------------+ +------------------+
```
In the picture above:
- There's a large box for the popcorn costing $7.25, representing the shared cost between the friends.
- Each of the four smaller boxes represents one movie ticket, each costing \(m\).
- The total cost of the tickets and popcorn equals $45.25, as described by the equation \(4m + 7.25 = 45.25\).
The correct representation of this scenario can be expressed in the following way:
1. The total cost of the tickets for 4 friends is \(4m\) (where \(m\) represents the cost of one ticket).
2. We add the cost of the popcorn ($7.25) to that total.
3. The equation to represent this situation is:
\[ 4m + 7.25 = 45.25 \]
Thus, the correct answer is:
**D. \(4m + 7.25 = 45.25\)**
Now we can solve for \(m\):
1. Subtract 7.25 from both sides:
\[
4m + 7.25 - 7.25 = 45.25 - 7.25
\]
\[
4m = 38.00
\]
2. Divide both sides by 4:
\[
m = \frac{38.00}{4} = 9.50
\]
So, the cost of one movie ticket is **$9.50**.
### Drawing a Picture to Model the Equation
You can visualize this equation as follows:
```
+--------------------+
| |
| Popcorn | $7.25
| |
+--------------------+
+------------------+ +------------------+ +------------------+ +------------------+
| | | | | | | |
| Movie Ticket 1| | Movie Ticket 2| | Movie Ticket 3| | Movie Ticket 4|
| (m) | | (m) | | (m) | | (m) |
| | | | | | | |
+------------------+ +------------------+ +------------------+ +------------------+
```
In the picture above:
- There's a large box for the popcorn costing $7.25, representing the shared cost between the friends.
- Each of the four smaller boxes represents one movie ticket, each costing \(m\).
- The total cost of the tickets and popcorn equals $45.25, as described by the equation \(4m + 7.25 = 45.25\).