Question

At a basketball game, 45% of people attending were supporting the home team, while 55% were supporting the visiting team. If 1413 people attending the game supported the home team, what was the total number of people attending the game?

Answer 1

Let \( x \) be the total number of people attending the game. According to the problem, 45% of the total attendance supports the home team. Therefore, we can express this mathematically as:

\[
0.45x = 1413
\]

To find \( x \), we can solve for it by dividing both sides by 0.45:

\[
x = \frac{1413}{0.45}
\]

Now, performing the division:

\[
x = 3135.555\ldots
\]

Since \( x \) must be a whole number (as you can't have a fraction of a person), we need to check our calculations more carefully. Let's perform the division step by step.

Calculating \( \frac{1413}{0.45} \):

1. First, we can multiply both the numerator and the denominator by 100 to clear the decimal:

\[
\frac{1413 \times 100}{0.45 \times 100} = \frac{141300}{45}
\]

2. Now, we can perform the division \( 141300 \div 45 \):

\[
141300 \div 45 = 3140
\]

Thus, the total number of people attending the game is:

\[
\boxed{3140}
\]

To verify:

Calculating 45% of 3140 gives:

\[
0.45 \times 3140 = 1413
\]

This confirms that our answer is correct: the total number of people attending the game is indeed \( \boxed{3140} \).