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Cheque paid with dollars and cents swapped

Question

A bank clerk cashing a man's cheque mixed up the units: the cents figure was paid out as dollars and the dollars figure as cents. The man, who arrived with no money, did not count it, bought a 5-cent sweet, and then found that what he had left was precisely double the cheque's face value. What was the cheque for?

Short answer

$31.63. Let the cheque be xx dollars and yy cents. Then 100y+x−5=2(100x+y)100y+x-5=2(100x+y), i.e. 98y=199x+598y=199x+5, whose solution with 0≤y≤990\le y\le 99 is x=31x=31, y=63y=63. Check: he received $63.31, and after 5 cents has $63.26, twice $31.63.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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