Question

Eight hundred tickets are sold for a play. Thirty-five percent of those tickets were sold in advance. Which equation can be used to find the number of tickets sold in advance?
StartFraction 800 divided by 8 Over 35 divided by 8 EndFraction = StartFraction 100 Over 4.375 EndFraction
StartFraction 100 divided by 8 Over 800 divided by 8 EndFraction = StartFraction 12.5 Over 100 EndFraction
StartFraction 35 times 8 Over 800 times 8 EndFraction = StartFraction 280 Over 6400 EndFraction
StartFraction 35 times 8 Over 100 times 8 EndFraction = StartFraction 280 Over 800 EndFraction

Answer 1

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:

1. **Converting percentages to fractions**: 35% can be expressed as \(\frac{35}{100}\).
2. **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:

1. **Option A**: \(\frac{800}{8} \div \frac{35}{8}\) does not simplify to finding the number of advance tickets.
2. **Option B**: \(\frac{100}{8} \div \frac{800}{8}\) also does not represent the correct calculation.
3. **Option C**: \(\frac{35 \times 8}{800 \times 8}\) does not provide a meaningful way to deduce the number of advance tickets.
4. **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**.