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

1 answer

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.