Question

Multiple Representations  A group of 5 friends went to the movies. In addition to their​ tickets, they bought a large bag of popcorn to share for ​$6.25. The total was ​$43.75. 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.
5minus6.25mequals43.75
B.
6.25minus5mequals43.75
C.
6.25mplus5equals43.75
D.
5mplus6.25equals43.75

Answer 1

To find the cost of one movie ticket, we need to account for the total cost of the tickets and the popcorn.

Let \( m \) represent the cost of one movie ticket. Since there are 5 friends, the total cost of the tickets will be \( 5m \). We also need to add the cost of the popcorn, which is $6.25.

The total cost of the movies plus popcorn is $43.75. Therefore, we can write the equation as:

\[
5m + 6.25 = 43.75
\]

So the correct choice is:

D. \( 5m + 6.25 = 43.75 \)

### Part 2: Solving the Equation

To solve the equation \( 5m + 6.25 = 43.75 \):

1. Subtract \( 6.25 \) from both sides:
\[
5m = 43.75 - 6.25
\]
\[
5m = 37.50
\]

2. Divide both sides by \( 5 \):
\[
m = \frac{37.50}{5}
\]
\[
m = 7.50
\]

Thus, the cost of one movie ticket \( m \) is **$7.50**.

### Picture Representation

To visually represent this equation, you might draw:

1. A rectangle labeled "Popcorn" with a value of $6.25 to show the cost of the popcorn.
2. Five smaller rectangles labeled "Ticket" each representing one movie ticket at an undetermined cost \( m \).
3. An arrow pointing from the sum of these costs to a box labeled "Total Cost" with a value of $43.75, showing that \( 5m + 6.25 = 43.75 \).

This visual will help reflect the components contributing to the total cost.