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The sum of digits in a two digit number formed by two digits from 1 to 9 is 8. If 9 is added to a number then both the digits become equal. find the number.​

Answer :

danielmaduroh

Explanation:

Here we need to set a system of two linear equations in two variables. So:

  • The sum of digits in a two digit number formed by two digits from 1 to 9 is 8:

Let [tex]x \ and \ y[/tex] be those digits, then:

[tex]x+y=8 \ \ldots eq1[/tex]

  • If 9 is added to a number then both the digits become equal. find the number:

[tex]10x+y+9 \ldots expression \ 1[/tex]

But from eq 1:

[tex]y=8-x[/tex]

Substituting y into the expression 1:

[tex]10x+(8-x)+9=9x+17[/tex]

The x-value will be found by hit and trial, so:

  • Let x = 1:

[tex]9x + 17 = 9(1)+17 = 26[/tex]

We have to reject this solution because digits are different.

  • Let x = 2:

[tex]9x + 17 = 9(2)+17 = 35[/tex]

We have to reject this solution because digits are different.

  • Let x = 3:

[tex]9x + 17 = 9(3)+17 = 44[/tex]

Then this is a two digit number formed by two equal digits.

Finally, the number is:

44

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