The sum of the digits of a 2-digit number is 11. If the digits are reversed, the number formed is 45 more than the original number. Find the original number

Step-by-step explanation:

Let the two-digit number be 10t+u where t is the tens digit and u the units digit.

EQUATION:

t+u = 11

10u+t = 10t+u + 45

Rearrange the equations:

t+u = 11

9t-9u = -45

Simplify:

t+u = 11

t-u = -5

Add the equations to solve for "t":

2t = 6

t = 3

Substitute to solve for "u":

3+u = 11

u = 8

15

step-by-step explanation: