Let n be the number
1/n = reciprocal of the number
Equation:
n - 30(1/n) = 1
(n) (n) - 30 (n) = (1)(n)
n
n² - 30 = n
n² - n - 30 = 0
Solve by factoring:
(n - 6) (n + 5) = 0
n-6 = 0 n+5 = 0
n = 6 n = -5
The problem is looking for natural number, so choose the positive solution/rrot which is n= 6
Final Answer: The natural number is 6.
TO Check:
n - 30(1/n) = 1
6 - 30 (1/6) = 1
6 - (30/6) = 1
6 - 5 = 1
1 = 1