Final answer:
To solve the problem, we need to represent the unknown number as 'x' and set up an equation. By manipulating the equation, we can solve for 'x' and find the correct value. The answer is a) 23.
Step-by-step explanation:
To solve this problem, let's represent the unknown number as 'x'. The problem states that the sum of the positive number and 47 is 1088 times the reciprocal of the number. We can write this as:
x + 47 = 1088 * (1/x)
To solve for 'x', we need to isolate it on one side of the equation. We can start by multiplying both sides of the equation by 'x' to eliminate the fraction:
x^2 + 47x = 1088
Next, we can rearrange the equation into a quadratic form:
x^2 + 47x - 1088 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, the equation factors as:
(x - 23)(x + 47) = 0
So, the possible values for 'x' are 23 and -47. Since the prompt asks for a positive number, the answer is 23. Therefore, the correct option is a) 23.