Final answer:
The given problem requires solving an equation to find a two-digit number. However, after solving the equation, it is determined that there is no valid solution to the problem.
Step-by-step explanation:
The problem states that a number obtained by increasing 75% of a given two-digit number is 8 more than half of another two-digit number formed by reversing the digits of the given number. Let's solve for the given number using algebraic equations:
- Let the given two-digit number be represented as 10x + y, where x is the tens digit and y is the units digit.
- According to the problem, 1.75(10x + y) = 0.5(10y + x) + 8.
- Simplifying the equation, we get 17x + 7y = 5y + x + 8.
- Combining like terms, we have 16x + 2y = 8.
- Since the number is a two-digit number, x cannot be 0. Therefore, x must be 1.
- Substituting x = 1 into the equation, we get 16(1) + 2y = 8.
- Simplifying the equation further, we have 2y = -8.
- Dividing both sides by 2, we obtain y = -4.
- The sum of the digits of the given number is 1 + (-4) = -3.
Since the sum of digits cannot be negative, we discard this solution.
Therefore, there is no valid answer to this problem.