Mr. and Mrs. Garcia took their three children to see a matinee on Saturday . They spent a total of $55.50,1 which included $29.25 at the concession stand. Each of the movie tickets cost the same amount. Which equation shows the cost of each ticket,t ?
The Correct Answer and Explanation is :
To determine the cost of each movie ticket, we can break down the total cost of the outing into two parts: the cost of the movie tickets and the cost at the concession stand.
We know:
- The total spent was $55.50.
- The total spent at the concession stand was $29.25.
- The remaining amount was spent on movie tickets.
Step 1: Subtract the concession cost
The total cost of the movie tickets is the remaining amount after the concession cost:
[
\text{Total cost of tickets} = 55.50 – 29.25 = 26.25
]
Step 2: Define the number of tickets
Mr. and Mrs. Garcia bought tickets for themselves and their three children, so they purchased 5 tickets in total.
Step 3: Set up the equation
Let the cost of each ticket be ( t ). The total cost of the tickets for all five people is:
[
5 \cdot t = 26.25
]
Step 4: Solve for ( t )
To find the cost of each ticket, divide both sides of the equation by 5:
[
t = \frac{26.25}{5} = 5.25
]
Thus, the cost of each movie ticket is $5.25.
Final Equation
The equation that shows the cost of each ticket is:
[
5t = 26.25
]
Explanation:
In this problem, we used basic algebra to break down the total cost into the two known parts: the concession and the tickets. By subtracting the concession cost from the total spent, we were left with the cost of the movie tickets. Since the tickets cost the same amount for each person, the total ticket cost was split equally among the five people. By setting up the equation ( 5t = 26.25 ), we were able to solve for ( t ), which represents the cost of each ticket. This approach is a good example of applying algebra to real-life situations, like budgeting for a family outing.