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In a certain flight 3/4 of its seats were booked, including
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17 May 2025, 01:27
17 May 2025, 01:27
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In a certain flight $\(\frac{3}{4}\)$ of its seats were booked, including $\(\frac{2}{3}\)$ of its business class seats. If $\(\frac{3}{5}\)$ of its seats were business class, then what percent of the seats that were not booked were business class?
(A) $\(20 \%\)$
(B) $\(33 \frac{1}{3} \%\)$
(C) $\(35 \%\)$
(D) $\(45 \%\)$
(E) $\(80 \%\)$
(A) $\(20 \%\)$
(B) $\(33 \frac{1}{3} \%\)$
(C) $\(35 \%\)$
(D) $\(45 \%\)$
(E) $\(80 \%\)$
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Re: In a certain flight 3/4 of its seats were booked, including
[#permalink]
20 May 2025, 04:30
20 May 2025, 04:30
Expert Reply
We are given the following information about a flight:
1. Total seats booked: $\(\frac{3}{4}\)$ of all seats.
2. Business class seats booked: $\(\frac{2}{3}\)$ of all business class seats.
3. Business class seats as a fraction of total seats: $\(\frac{3}{5}\)$.
We need to find the percentage of unbooked seats that are business class.
Step 1: Assign a Total Number of Seats
To simplify calculations, let's assume the flight has $\(\mathbf{6 0}\)$ seats (a common multiple of the denominators 4, 3, and 5).
Step 2: Calculate Key Quantities
1. Total seats booked:
$$
\(\frac{3}{4} \times 60=45 \text { seats }\)
$$
2. Total business class seats:
$$
\(\frac{3}{5} \times 60=36 \text { seats }\)
$$
3. Business class seats booked:
$$
\(\frac{2}{3} \times 36=24 \text { seats }\)
$$
4. Non-business class seats:
$$
\(60-36=24 \text { seats }\)
$$
5. Non-business class seats booked:
Total booked - Business class booked $\(=45-24=21\)$ seats
6. Total unbooked seats:
$$
\(60-45=15 \text { seats }\)
$$
7. Unbooked business class seats:
Total business class - Business class booked $\(=36-24=12\)$ seats
Step 3: Compute the Required Percentage
We need the percentage of unbooked seats that are business class:
$$
\(\frac{\text { Unbooked business class seats }}{\text { Total unbooked seats }} \times 100=\frac{12}{15} \times 100=80 \%\)
$$
1. Total seats booked: $\(\frac{3}{4}\)$ of all seats.
2. Business class seats booked: $\(\frac{2}{3}\)$ of all business class seats.
3. Business class seats as a fraction of total seats: $\(\frac{3}{5}\)$.
We need to find the percentage of unbooked seats that are business class.
Step 1: Assign a Total Number of Seats
To simplify calculations, let's assume the flight has $\(\mathbf{6 0}\)$ seats (a common multiple of the denominators 4, 3, and 5).
Step 2: Calculate Key Quantities
1. Total seats booked:
$$
\(\frac{3}{4} \times 60=45 \text { seats }\)
$$
2. Total business class seats:
$$
\(\frac{3}{5} \times 60=36 \text { seats }\)
$$
3. Business class seats booked:
$$
\(\frac{2}{3} \times 36=24 \text { seats }\)
$$
4. Non-business class seats:
$$
\(60-36=24 \text { seats }\)
$$
5. Non-business class seats booked:
Total booked - Business class booked $\(=45-24=21\)$ seats
6. Total unbooked seats:
$$
\(60-45=15 \text { seats }\)
$$
7. Unbooked business class seats:
Total business class - Business class booked $\(=36-24=12\)$ seats
Step 3: Compute the Required Percentage
We need the percentage of unbooked seats that are business class:
$$
\(\frac{\text { Unbooked business class seats }}{\text { Total unbooked seats }} \times 100=\frac{12}{15} \times 100=80 \%\)
$$
gmatclubot
Re: In a certain flight 3/4 of its seats were booked, including [#permalink]
20 May 2025, 04:30
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