"the sum of the digits of a two-digit number is 13. reversing the digits produces a number that is 9 less than the original number. what is the original number?"

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03-11-2017
Mathematics

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"the sum of the digits of a two-digit number is 13. reversing the digits produces a number that is 9 less than the original number. what is the original number?"

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tynollette tynollette · Answer 1 · 2017-11-03T05:55:10+01:00

tynollette tynollette

03-11-2017

suppose the one's digit is x, the ten's digit is y. the original number is 10y+x, the reversed number is 10x+y

x+y=13
(10x+y)=(10y+x)-9 =>9y-9x=9 =>y-x=1
Add the two equation to solve: 2y=14 =>y=7
x=13-7=6
the original number is 76.

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