Airport connundrum

Number Theory Level pending

An airline receptionist lost her records to flight ABC 123. She knows that everyone paid the same integer number of pounds for the flight to Phillippines, and the total collected is £1,000,009. Given that the airplane holds at most 300 people, and the ticket costs at most £5,000, how many people paid for a ticket?


The answer is 293.

Andrew Gray by Andrew Gray , 17, United Kingdom

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1 solution

Andrew Gray
Nov 22, 2017

If we take the number of pounds collected, that is 1000009 and factorise it on a calculator, we find that 293 people went and they each paid £3413.

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Yes, although there could have been only 1 person who paid £1000009. Furthermore, the question should be "how many people", as what to input as one's answer is confusing.

Stephen Mellor - 3 years, 6 months ago

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Yes, sorry; I thought that by asking how many people went that it implied a number - and one person would hardly have boarded the plane alone to pay just over £1m. The point of adding the information that the plane held 300 people was to provide a limit in the number; and the rest can be worked out by using decision and discreet mathematics.

Andrew Gray - 3 years, 6 months ago

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... 1 is a number. Also, the question phrasing is still confusing

Stephen Mellor - 3 years, 6 months ago

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