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:
- 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
To find which equation can be used to represent the situation, we can analyze them:
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\( \frac{800}{40} \div \frac{40}{40} = \frac{800}{40} = 20 \): This doesn’t seem to provide useful information for finding total tickets.
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\( \frac{100/4}{800/4} = \frac{25}{200} = \frac{1}{8} \): This also isn’t helpful.
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\( \frac{40 \times 20}{800 \times 20} = \frac{800}{16,000} \): Simplifies to \( \frac{1}{20} \), which doesn't help either.
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\( \frac{40 \times 20}{100 \times 20} = \frac{800}{2000} \): 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.
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