Question

The units digit of a two digit number is 1 more than twice the tens digit. If the digits are reversed, the new number is 36 more than the original number. Find the number.

Answer 1

Answer:

37

Step-by-step explanation:

Let the initial number be $xy=10x+y$.

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

$y=2x+1$

Reversed number is $yx=10y+x.$

If the new number is 36 more than the original number, then

$(10y+x)-(10x+y)=36$

Simplify this equation:

$10y+x-10x-y=36\\ \\9y-9x=36\\ \\y-x=4$

Substitute $y=2x+1$ into the equation $y-x=4:$

$(2x+1)-x=4\\ \\2x+1-x=4\\ \\x+1=4\\ \\x=3\\ \\y=2\cdot 3+1=7$

Initial number: 37