Answer:
37
Step-by-step explanation:
Let the initial number be [tex]xy=10x+y[/tex].
Initial number:
Units digit = y
Tens digit = x
The units digit of a 2-digit number is 1 more than twice the tens digit, then
[tex]y=2x+1[/tex]
Reversed number is [tex]yx=10y+x.[/tex]
If the new number is 36 more than the original number, then
[tex](10y+x)-(10x+y)=36[/tex]
Simplify this equation:
[tex]10y+x-10x-y=36\\ \\9y-9x=36\\ \\y-x=4[/tex]
Substitute [tex]y=2x+1[/tex] into the equation [tex]y-x=4:[/tex]
[tex](2x+1)-x=4\\ \\2x+1-x=4\\ \\x+1=4\\ \\x=3\\ \\y=2\cdot 3+1=7[/tex]
Initial number: 37
