Question

Sports A hockey arena has a seating capacity of \(30,275 .\) Of these seats, about \(31 \%\) are taken by season ticket holders. About how many seats are taken by season ticket holders?

Short answer

Approximately 9,485 seats are taken by season ticket holders.

Step-by-step solution

Understand the Problem

To find the number of seats taken by season ticket holders, start by identifying the given values: the total seating capacity and the percentage of these seats occupied by season ticket holders.

Identify the Given Values

The total seating capacity of the hockey arena is 30,275 seats and 31% of these seats are taken by season ticket holders.

Convert Percentage to Decimal

To work with percentages in calculations, convert the percentage to a decimal. For 31%, divide by 100: \[ 31 \, \% = \frac{31}{100} = 0.31 \]

Calculate the Number of Seats Taken by Season Ticket Holders

Multiply the total number of seats by the decimal conversion of the percentage:\[ 30,275 \times 0.31 = 9,485.25 \]

Interpret the Result

Since the number of seats must be a whole number, round the result to the nearest whole number. So, approximately 9,485 seats are taken by season ticket holders.

Key concepts

percentage conversion

Converting percentages into decimals is a crucial step when dealing with percentages in algebra problems. It allows us to use straightforward arithmetic operations to solve problems. To convert a percentage into a decimal, you simply divide the percentage by 100. For example, if you have 31%, you calculate: \( 31 \, \% = \frac{31}{100} = 0.31 \). This conversion is essential for further calculations, such as multiplying the total numbers to find portions or parts of a whole. Always remember: converting before calculating ensures accuracy.

seating capacity calculation

To determine how many seats are occupied in an arena or any venue, we need to understand seating capacity and make calculations based on percentages. In our specific example, the hockey arena has a total seating capacity of 30,275 seats. The problem states that 31% of these seats are occupied by season ticket holders. To find the actual number of seats taken, we must use the decimal form of the percentage we calculated earlier. We then multiply this decimal by the total seating capacity to find the specific number of seats:
\( 30,275 \times 0.31 \). Since seat counts must be whole numbers, rounding the result to the nearest integer is necessary. This results in approximately 9,485 seats being occupied by season ticket holders.

multiplying decimals

Multiplying decimals is another fundamental concept in solving algebra problems, especially when percentages are involved. Once the percentage is converted to a decimal, you often need to multiply this decimal by another number to find your answer. In our exercise, after converting 31% to 0.31, we multiply by the seating capacity:
\( 30,275 \times 0.31 = 9,485.25 \). While this gives a precise value, be mindful of context—in this case, since we’re counting seats, we must round to the nearest whole number, getting 9,485. Remember, handle decimals carefully to ensure accurate results in your calculations.