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 \( \frac{1413}{0.45} \):
- First, we can multiply both the numerator and the denominator by 100 to clear the decimal:
\[ \frac{1413 \times 100}{0.45 \times 100} = \frac{141300}{45} \]
- 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 \( \boxed{3140} \).
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