Question

Find a positive number which when increased by 11 is equal to 60 times the reciprocal of the number

Answer 1

Hi!☺

Let the positive number be x.

By the given condition,

x + 11 = 60(1/x)

x + 11 = 60/x

x(x + 11) = 60

x^2 + 11x = 60

x^2 + 11x - 60 = 0

[By factorization method]

x^2 + 15x - 4x - 60 = 0

x(x+15) - 4(x+15) = 0

(x+15)(x-4) = 0

So.,
x + 15 = 0 OR. x - 4 = 0

We get,
x = -15. Or. x=4

But x = -15 is not acceptable.

Thus,
x = 4
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Final Answer:
The positive number is 4.
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Hope this Helps !