Final answer:
To find the two-digit number, we can set up a system of equations based on the given information. Solving these equations simultaneously will help us find the answer. The correct answer is 92.
Step-by-step explanation:
To find the two-digit number, let's assign variables. Let the tens digit be 'x' and the units digit be 'y.' The number can be represented as 10x + y. The problem states that the sum of the digits is 11, so we have the equation x + y = 11.
Reversing the digits gives us 10y + x. The problem also states that this reversed number is 45 less than the original number. So we have the equation 10x + y - (10y + x) = 45.
Simplifying the equation, we get 9x - 9y = 45. Dividing both sides by 9, we have x - y = 5.
Now we have a system of equations: x + y = 11 and x - y = 5. Solving these equations simultaneously, we can add the two equations to eliminate the variable y. Adding x + y = 11 and x - y = 5 gives us 2x = 16. Dividing both sides by 2, we find that x = 8. Substituting this value back into x + y = 11, we get 8 + y = 11. Solving for y, we find that y = 3.
Therefore, the two-digit number is 83. The correct answer is (d) 92.