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ahrayia [7]
3 years ago
11

Please help! Hi, I'm stuck on a part of this question, we have to solve using Gauss Jordan Elimination: A corporation wants to l

ease 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?
Mathematics
1 answer:
RUDIKE [14]3 years ago
8 0
Do common sense has anything to do with this question? Because 
<span>corporation might forget the arbitrary 12 airplane rule </span>
<span>and have 11 times 20 = 220. </span>
<span>But perhaps they get a discount if all 12 hangars are used! </span>

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

<span>a + b + c = 12 </span>
<span>10a +15b +20c = 220 </span>

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

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

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

<span>One that carries 10, 2 that carries 15, and 9 that carries 20 </span>
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