Question

At a college football game, \(\frac{4}{5}\) of the seats in the lower deck of the stadium were sold. If \(\frac{1}{4}\) of all the seating in the stadium is located in the lower deck, and if \(\frac{2}{3}\) of all the seats in the stadium were sold, then what fraction of the unsold seats in the stadium was in the lower deck ?

• A. \(\frac{3}{20}\)
• B. \(\frac{1}{6}\)
• C. \(\frac{1}{5}\)
• D. \(\frac{1}{3}\)

Answer 1

The Correct Option is A

To determine the fraction of unsold seats in the stadium that were in the lower deck, follow these steps:

1. Define the total number of seats in the stadium as \(S\).
2. The portion of seats located in the lower deck is \(\frac{1}{4}\) of all the seats: \(\frac{1}{4}S\).
3. Since \(\frac{4}{5}\) of the lower deck seats were sold, the number of unsold seats in the lower deck is the remaining \(\frac{1}{5}\) of the lower deck seats: \(\frac{1}{5} \times \frac{1}{4}S = \frac{1}{20}S\).
4. Overall, \(\frac{2}{3}\) of the total stadium seats were sold. So, the unsold seats in the entire stadium are the remaining \(\frac{1}{3}\) of the total seats: \(\frac{1}{3}S\).
5. To find the fraction of unsold seats in the stadium that were in the lower deck, divide the unsold lower deck seats by the total unsold seats in the stadium:
   \[\frac{\text{Unsold Lower Deck Seats}}{\text{Total Unsold Seats in Stadium}} = \frac{\frac{1}{20}S}{\frac{1}{3}S} = \frac{1}{20} \div \frac{1}{3} = \frac{1}{20} \times \frac{3}{1} = \frac{3}{20}\]
6. The fraction of the unsold seats in the stadium that were in the lower deck is \(\frac{3}{20}\).