Final answer:
The positive number that, when increased by 17, equals 60 times its reciprocal is 3. The equation is set up and solved by factoring the quadratic equation, resulting in the solution x = 3.
Step-by-step explanation:
The question asks to find a positive number that when increased by 17 is equal to 60 times its reciprocal. First, we set up the equation x + 17 = 60(1/x), where x is the unknown positive number.
Next, we multiply both sides of the equation by x to get rid of the fraction: x^2 + 17x = 60. Now, we bring all terms to one side to form a quadratic equation: x^2 + 17x - 60 = 0.
We can factor this equation as (x - 3)(x + 20) = 0. Setting each factor equal to zero gives us two possible solutions for x: x = 3 or x = -20. Since we are looking for a positive number, we select x = 3 as the correct answer.