The sum of number of a two-digit number is 8. If 36 is added to the number climate the number reversed. Discover the number.

You are watching: The sum of the digits of a two-digit number is 8 Given :

The sum of the digits of a two-digit number is 8, if 36 is included to the number the digits obtain reversed.

To discover :

We have actually to find the number.

Solution :

Let the number it is in \$10x+y\$.

\$x+y=8\$

It is additionally given the if 36 is added to the number the digits gets reversed.

Therefore,

\$10x+y+36 = 10y+x\$

\$10y+x-10x-y = 36\$

\$10y-y+x-10x= 36\$

\$9y-x(10-1)=36\$

\$9y-9x=36\$

\$9(y-x)=36\$

\$y-x=frac369\$

\$y-x=4\$

\$y-x=4\$ and \$x+y=8\$

\$y-x+x+y=4+8\$

\$2y=12\$

\$y=frac122\$

\$y=6\$

\$x+6=8\$

\$x=8-6\$

\$x=2\$

The initial number is \$10(2)+6=20+6=26\$.

Therefore, the number is 26.

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