Question

In a two-digit number, the tens digit is two less than the units digit. If the digits are reversed, the sum of the reversed number and the original number is 154. Find the original number.

Answer 1

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Answer 2

Denote the number by
`10a+b`, where
`a,b` are positive integers between 0 and 9
`(a\\eq0)`.

"the tens digit is two less than the units digit"
`\implies a=b-2`

Reversing digits gives a new number
`10b+a`.

"sum of the reversed number and the original number is 154"
`\implies10(a+b)+(b+a)=154`

Simplify the second equation:

`11(a+b)=154\implies a+b=(154)/(11)=14`

Since
`a=b-2`, by substitution we get

`(b-2)+b=2b-2=2(b-1)=14\implies b-1=\frac{14}2=7\implies b=8`

which in turn gives

`a=8-2=6`

So the original number is
`10\cdot6+8=68`.