Final answer:
The original number is 58. The first digit is 5 as given, and by forming an equation based on the conditions and solving for the second digit, we find that it is 8.
Step-by-step explanation:
The question involves solving a basic algebraic problem to determine a two-digit number based on the given conditions. We know that the first digit is 5, and when the digits are switched, the new number is 27 greater than the original number. Let's denote the second digit of the number as 'x' and the original number as 10 × 5 + x (since the first digit contributes to the tens place and the second digit to the ones place).
When we switch the digits, the number becomes 10 × x + 5. According to the problem, the reversed number is 27 greater than the original, hence:
10 × x + 5 = (10 × 5 + x) + 27
Expanding both sides gives:
10x + 5 = 50 + x + 27
Combining like terms and simplifying:
10x + 5 = 77 + x
9x = 72
Dividing both sides by 9 to find the value of 'x':
x = 8
So, the second digit 'x' is 8, making the original number 58. Indeed, reversing the digits gives us 85, which is 27 greater than 58.