Perhaps easiest to understand is the most straightforward: figure the total number of seats and the number of seats being used. Check to see if that is more than half.

The 1 first-class carriage has usage of ...

(3/8)(64 seats) = 24 seats.

The 6 standard carriages have usage of ...

(7/13)(6 · 78 seats) = 252 seats.

The total number of seats used is ...

24 + 252 = 276 . . . . seats used

The total number of seats on the train is ...

1·64 +6·78 = 532 . . . . seats on the train

Half of the seats on the train will be ...

532/2 = 266 seats . . . . half the seats

The 276 used seats are more than half of the total number. More than half the seats are being used.

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Alternate solution

Another way to look at this is to compare utilization to 1/2 in each carriage class.

In first class 1/2 -3/8 = 1/8 of 64 seats = 8 seats fewer than 1/2 the seats are being used.

In standard class, 7/13 -1/2 = 14/26 -13/26 = 1/26 of 78 seats = 3 seats more than 1/2 the seats are being used. There are 6 standard class carriages, so 6·3 = 18 more than half the seats in the standard-class carriages are being used.

This number is 10 more than the 8 under-utilized seats in first class, so more than half the train seats are being used.

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2 years ago