To find the total number of tickets sold for the entire day when we know that 800 tickets represent 40 percent of the total tickets, we can use the formula:
\[ \text{Total Tickets} = \frac{\text{Tickets Sold}}{\text{Percentage Sold}} \]
In this case, the calculation would be:
\[ \text{Total Tickets} = \frac{800}{0.40} \]
Rearranging that in fraction form yields:
\[ \frac{800}{40} = \frac{800 \times 100}{40 \times 100} = \frac{80000}{4000} \]
So we can look for a similar fraction in the provided options.
We can simplify \(800 \div 40\) to find the fraction:
\[ \frac{800}{40} = 20 \text{ (which represents 100 percent of the tickets)} \]
Now let's evaluate the options to find out which represents this relationship correctly.
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First option:
\(\frac{800}{40} = \frac{20}{1}\)
This suggests that \(800\) represents40%, which aligns with our understanding. This option correctly illustrates the calculations we need to arrive at the total, as it directly finds the relationship between the sold tickets and the percentage. -
Second option:
\(\frac{100}{4} = \frac{800}{4}\)
This statement does not correspond directly to our equation we want to assess. -
Third option:
\(\frac{40 \times 20}{800 \times 20} = \frac{800}{16000}\)
This does not help us relate ticket sales to total sales effectively. -
Fourth option:
\(\frac{40 \times 20}{100 \times 20} = \frac{800}{2000}\)
This again doesn’t provide the correct equation to find the total tickets.
The best option given to find the total number of tickets sold for the entire day from the information given is:
1. \(\frac{800}{40} = \frac{20}{1}\)
This option effectively demonstrates that you can derive the total using the number of tickets sold and the percentage they represent.