Question

Please help! Hi, I'm stuck on a part of this question, we have to solve using Gauss Jordan Elimination: A corporation wants to lease a fleet of 12 airplanes with a combined carrying capacity of 220 passengers. The three available types of planes carry 10,15,20 passengers. How many of each type of plane should be leased?

Answer 1

Do common sense has anything to do with this question? Because
corporation might forget the arbitrary 12 airplane rule
and have 11 times 20 = 220.
But perhaps they get a discount if all 12 hangars are used!

Playing by the rules of the question:-
Let a, b, c be the aeroplanes that carry
10, 15, and 20 passengers, respectively,

a + b + c = 12
10a +15b +20c = 220

We may rearrange these as
4a + 4b + 4c = 48
2a + 3b + 4c = 44
Now subtract
2a + b = 4

There appear to be 3 options
a = 0, b = 4 which means 220 = 0*10 + 4*15 + 8*20
a = 1, b = 2 which means 220 = 1*10 + 2*15 + 9*20
a = 2, b = 0 which means 220 = 2*10 + 0*15 + 7*20

If you dismiss the ones with zeros it may be that
the expected answer to "How many of each plane" is

One that carries 10, 2 that carries 15, and 9 that carries 20