To find the number of tickets sold in advance, we need to calculate 35% of 800 tickets. The equation we can use to represent this is:
\[ \text{Number of tickets sold in advance} = 0.35 \times 800 \]
To translate this into an equation that resembles the options presented, let's break it down:
- Converting percentages to fractions: 35% can be expressed as \(\frac{35}{100}\).
- Applying this to the total tickets sold: The number of tickets sold in advance can thus be represented as: \[ \text{Number sold in advance} = \frac{35}{100} \times 800 \]
Now, if we simplify \(\frac{35}{100} \times 800\): \[ = \frac{35 \times 800}{100} \] This simplifies to: \[ = \frac{28000}{100} = 280 \]
Now let's check which of the given options fits:
- Option A: \(\frac{800}{8} \div \frac{35}{8}\) does not simplify to finding the number of advance tickets.
- Option B: \(\frac{100}{8} \div \frac{800}{8}\) also does not represent the correct calculation.
- Option C: \(\frac{35 \times 8}{800 \times 8}\) does not provide a meaningful way to deduce the number of advance tickets.
- Option D: \(\frac{35 \times 8}{100 \times 8}\) simplifies to \(\frac{35}{100}\), and allows calculation as follows:
- Since both terms are multiplied by 8, they can be factored out, leaving: \[ \frac{35}{100} = 0.35 \] Thus: \[ \frac{35 \times 8}{100 \times 8} = \frac{35}{100} \text{ which leads us to } 0.35 \times 800. \]
Thus the best option to represent \(35%\) of \(800\) tickets sold is:
\[ \text{Option D: } \frac{35 \times 8}{100 \times 8} = \frac{280}{800} \]
This means that the correct answer is Option D.