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Asked: April 7, 20212021-04-07T07:37:12+00:00 2021-04-07T07:37:12+00:00In: Middle School/Junior Secondary School

The sum of the digits of a two digit numbers is 12. Reversing its digit decreases the value by 36. What is the number?

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acedstud · Accepted Answer · 2021-04-14T10:27:38+00:00

Let the tens digit be $a$ and the ones digit be $b$ , then the number is given by $10a+b$ .

The sum of the digits is 12 means that $a+b=12$ . . . . . (1)

Reversing the digits, we have the number $10b+a$ .

Thus, “reversing the digits decreases the value by 36” means $10a+b-36=10b+a\Rightarrow10a-a+b-10b=36\Rightarrow9a-9b=36$ . . . . . (2)

From (1), $a=12-b$ , which when substituted into (2) gives $9(12-b)-9b=36\Rightarrow108-9b-9b=36\Rightarrow-18b=36-108=-72$ .

Dividing both sides by -18, we have $\dfrac{-18b}{-18}=\dfrac{-72}{-18}\Rightarrow b=4$ and $a=12-4=8$ .

Therefore, the number is $10(8)+4=80+4=84$ .

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