Question

At an amusement park, 40 percent of the tickets were sold in the first hour. If 800 tickets were sold in the first hour, which equation can be used to find the total number of tickets sold for the entire day?
StartFraction 800 divided by 40 Over 40 divided by 40 EndFraction = StartFraction 20 Over 1 EndFraction
StartFraction 100 divided by 4 Over 800 divided by 4 EndFraction = StartFraction 25 Over 200 EndFraction
StartFraction 40 times 20 Over 800 times 20 EndFraction = StartFraction 800 divided by 16,000 EndFraction
StartFraction 40 times 20 Over 100 times 20 EndFraction = StartFraction 800 Over 2000 EndFraction

Answer 1

To find the total number of tickets sold for the entire day given that 800 tickets represent 40% of the tickets sold, we can use the relationship between the percentage and the total amount.

If 800 tickets are 40% of the total tickets \( x \), then we can set up the equation:

\[
0.40x = 800
\]

To find \( x \), we can rearrange the equation:

\[
x = \frac{800}{0.40} = \frac{800 \times 100}{40} = \frac{80000}{40} = 2000
\]

Now, let's check which one of the provided equations reflects this situation:

1. StartFraction 800 divided by 40 Over 40 divided by 40 EndFraction = StartFraction 20 Over 1 EndFraction
2. StartFraction 100 divided by 4 Over 800 divided by 4 EndFraction = StartFraction 25 Over 200 EndFraction
3. StartFraction 40 times 20 Over 800 times 20 EndFraction = StartFraction 800 divided by 16,000 EndFraction
4. StartFraction 40 times 20 Over 100 times 20 EndFraction = StartFraction 800 Over 2000 EndFraction

To find which equation can be used to represent the situation, we can analyze them:

1. \( \frac{800}{40} \div \frac{40}{40} = \frac{800}{40} = 20 \): This doesn’t seem to provide useful information for finding total tickets.

2. \( \frac{100/4}{800/4} = \frac{25}{200} = \frac{1}{8} \): This also isn’t helpful.

3. \( \frac{40 \times 20}{800 \times 20} = \frac{800}{16,000} \): Simplifies to \( \frac{1}{20} \), which doesn't help either.

4. \( \frac{40 \times 20}{100 \times 20} = \frac{800}{2000} \): This simplifies to \( \frac{40}{100} \) or \( 0.4 \), consistent with the initial understanding that \( 800 \) represents \( 40\% \) of \( 2000 \).

Based on analysis, the correct equation representing the total number of tickets sold for the entire day (using the value obtained through analysis) is:

**\( StartFraction 40 times 20 Over 100 times 20 EndFraction = StartFraction 800 Over 2000 EndFraction \)**.

This equation shows that if 800 tickets sold is 40% of the total (2000), it represents the relationship accurately. Therefore, option 4 is the equation we can use to find the total number of tickets sold.