Math CentralQuandaries & Queries


Question from Lloyd, a student:

The sum of digits of a certain 2 digit number is 7.
Reversing its digits increases the number by 9.
Find the number

Hi Lloyd,

Suppose the units digit of the number is $n$ and the tens digit is $m,$ then the number is $10m + n.$

You know that $m + n = 7.$

What is the number obtained if you reverse the digits? This number is $9$ more than the original number. This gives you a second equation in $m$ and $n.$ Solve the pair of equations for $m$ and $n.$


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