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

37

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