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

1 answer

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.

  1. First option:
    \(\frac{800}{40} = \frac{20}{1}\)
    This suggests that \(800\) represents 40%, 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.

  2. Second option:
    \(\frac{100}{4} = \frac{800}{4}\)
    This statement does not correspond directly to our equation we want to assess.

  3. Third option:
    \(\frac{40 \times 20}{800 \times 20} = \frac{800}{16000}\)
    This does not help us relate ticket sales to total sales effectively.

  4. 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.