SOLUTION: A natural number is increased by 5 is equal to 36 times the reciprocal of the number. Find the number.
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Question 1070108: A natural number is increased by 5 is equal to 36 times the reciprocal of the number. Find the number.
Found 2 solutions by ankor@dixie-net.com, rothauserc:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
natural number is increased by 5 is equal to 36 times the reciprocal of the number.
n + 5 = 36 *
multiply both sides by n, results:
n^2 + 5n = 36
A quadratic equation
n^2 + 5n - 36 = 0
Factors
(n + 9)(n - 4) = 0
n = -9
but
n = +4 is the number
:
:
Check in original equation
4 + 5 = 36 *
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let n be the natural number, then
:
((n + 5) / 1) = (36 / n)
:
cross multiply fractions
:
n(n + 5) = 36
:
n^2 +5n -36 = 0
:
(n + 9) * (n - 4) = 0
:
Note that a natural number is a positive integer
:
n = -9, n = 4
:
we reject the negative number, -9 as a solution
:
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The natural number solution is 4
:
check answer
:
4 + 5 = (36 / 4)
:
9 = 9
:
our answer checks
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:
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