If a stadium seats 1,600 people and sells (2)/(4) of its seats, how many tickets does it sell?
The correct answer and explanation is :
To find out how many tickets the stadium sells, we need to determine what fraction of the total seating capacity is sold.
Step 1: Understand the Problem
The stadium has a total seating capacity of 1,600 seats. It sells 2/4 of its total seats.
First, let’s simplify the fraction 2/4:
- 2/4 is equivalent to 1/2 because dividing both the numerator and denominator by 2 gives us 1/2.
Thus, the stadium sells half of its total seats.
Step 2: Calculate the Number of Seats Sold
Now that we know the stadium sells half of its seats, we multiply the total number of seats by 1/2:
[
\text{Seats sold} = 1,600 \times \frac{1}{2} = 800
]
Step 3: Conclusion
The stadium sells 800 tickets.
Explanation of the Process
- Total Seating Capacity: The stadium has 1,600 seats, meaning if all seats were filled, there would be 1,600 ticket sales.
- Fraction of Seats Sold: The fraction of seats sold is given as 2/4. When simplified, this equals 1/2, meaning half of the seats are being sold. To calculate this fraction of the total number of seats, we multiply the total number of seats (1,600) by the fraction of seats being sold (1/2).
- Perform the Multiplication: Multiplying 1,600 by 1/2 gives 800, which tells us that 800 tickets are sold.
This method can be applied to any problem involving a fraction of a whole number. The key is understanding how to simplify fractions and then apply them to find a portion of a quantity.