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I got this answer wrong. I thought it was 55% but it seems the answer is different. Please can you have a look at this and tell me where have I gone wrong and it should be. Thanks in advance.

Q) Approximately what proportion of the total number of seats in all Buses and Trains are empty?

EDITED - I FORGOT TO INCLUDE MULTPLY CHOICES

A) 45% B) 50% C) 55% D) 60% E) 65%

*Assume For Buses* Average No of Vehicles per Day (000's) = 112 Average Distance Travelled by one Vehicle per Day (km) = 57 Average No of Seats = 55 Average Occupancy (%) = 57  *Assume For Trains* Average No of Vehicles per Day (000's) = 89 Average Distance Travelled by one Vehicle per Day (km) = 108 Average No of Seats = 430 Average Occupancy (%) = 44 

The steps I took are the following...

 Step 1- Find total seats for Buses and Trains == 55 + 430 = 485  Step 2 - Find number of empty seats for Buses == 100 - 57 = 43.              55 * 0.43 = 23.65  Step 3 - Find number of empty seats for Trains == 100 - 44 = 56.         430 * 0.56 = 240.8  Step 4 - 23.65 + 240.8 = 264.45.  Step 5 - 264.45 / 485 = 0.5452 * 100 = **55%** 

EDITED STILL NOT GETTING THIS RIGHT

2nd attempt

for buses 112000 * 55 / 112000 * 43 = 616000 / 48160000 = 0.127906976 for trains 89000 * 430 / 89000 * 56 = 38270000 / 4984000 = 0.76785714  0.127906976 + 0.76785714 / 485  = 7.806478405/ 485 = 0.016095831  < this is wrong 

3rd attempt

for buses 112000 * 55 / 112000 * 0.43 = 616000 / 48160 = 12.79069767 for trains 89000 * 430 / 89000 * 0.56 = 38270000 / 49840 = 76.78571429  12.79069767 + 76.78571429 = 89.57641196 / 485 = 0.184693632  < this is wrong 
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    You lost a zero in the numerator for buses, it should be 6160000. You should not divide by the 112000 then, and the 0.43 goes in the numerator, not the denominator. Generally when you use a slash for division, it is important to parenthesize afterward to avoid confusion.2011-11-21

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You need to find the total number of seats on all the buses by multiplying the number of buses by the seats/bus then the number of vacant bus seats using the percentage. Then similarly for trains. Your calculation would be correct if there is only one bus and only one train. The fact that there are many more buses makes the bus occupancy be weighted much higher than train occupancy.

Added: You should not be dividing by the number of buses or trains. The number of empty bus seats is 112000 * 55 * 0.43= 2,648,800. The number of empty train seats is 89000 * 430 * .56=21,431,200$ The proportion of empty seats is (112000 * 55 * 0.43 + 89000 * 430 * .56)/(112000 * 55 + 89000 * 430 )=0.542

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    I agree with the Answer above, 54,2 % ≈ 55 %2012-05-16