When 36 is added to a certain two-digit number, the results is the number with the digits reversed. The units' digit is one more than twice the tens' digit. Find the number .

37

Step-by-step explanation:

T = two digit number

X = first digit

Y = second digit

T = XY where XY are two numbers placed next to eachother rather than multiplied.

36 + XY = YX

The units' digit is one more than twice the tens' digit.

Y = 1 + 2X

Since Y is a 1 digit number it can't be greater than 9.

9 ≥ 1 + 2X

This means X can't be greater than 4.

9 - 1 ≥ 2X

8 ≥ 2X

8/2 ≥ X

4 ≥ X

If X = 1, Y = 3

36 + 13 = 48

If X = 2, Y = 5

36 + 25 = 58

If X = 3, Y = 7

36 + 37 = 73

If X = 4, Y = 9

36 + 49 = 88

37 is the reverse of 73

Therefore the number is 37