Answer: The sum of the digits of a two – digit number is 14. If the digits are reversed, the number increases by 36

Step-by-step explanation:

Verified answer

Let the two digit number be 10x + y

Sum of the digits = 14

[tex]⇒(x + y) = 14.......(1)[/tex]

[tex]10x + y + 36 = 10y + x \\ \\10x + y - (10y + x) = - 36 \\ \\ 10x + y - 10y - x = - 36 \\ \\ 10x - x + y - 10y = - 36 \\ \\ 9x - 9y = - 36 \\ \\ 9(x - y) = - 36 \\ \\ x - y = \frac{ - 36}{9} \\ \\ x - y = - 4.....(2)[/tex]

[tex]Adding \: (1) \: and \: (2), \: we \: get \\ \\ x + y = 14 \\ \\ x - y = - 4 \\ \\ \\ 2x = - 10 \\ \\ x = \frac{ - 10}{2} \\ \\ x = - 5[/tex]

[tex]x - y = - 4 \\ \\ - 4 - y = - 4 \\ \\ y = - 4 + 4 \\ \\ y = 0[/tex]

[tex]The \: required \: number \: is  \\ \\ = 10x + y \\ \\ = 10( - 4) + 0 \\ \\ = - 40[/tex]