Answer :
To determine the total number of fans at the hockey game, we can set up a proportion. Given that the first 1,000 fans received a free hat and this represents 8% of the total number of fans, we can use the following steps to calculate the total number of fans:
1. Let's call the total number of fans "T."
2. We know that 8% of the total number of fans is equal to 1,000, which can be represented by the following equation:
\( 0.08 \times T = 1,000 \)
3. To solve for "T," we'll divide both sides of the equation by 0.08 to isolate "T" on one side of the equation:
\( T = \dfrac{1,000}{0.08} \)
4. Before performing the division, let's convert 0.08 to a fraction to make it easier to see what's happening. The fraction that represents 8% as a decimal is 8/100, which simplifies to 1/12.5. However, it's easier to work with decimals in this case, so we'll stick with 0.08.
5. Now we can divide 1,000 by 0.08:
\( T = \dfrac{1,000}{0.08} \)
6. Performing this division (you can use a calculator or long division), you'll get:
\( T = 12,500 \)
So there were a total of 12,500 fans at the hockey game.
