Question

Find the whole number which when increased by 20 is equal to 69 times the reciprocal of the number

Answer 1

Let the whole number be x
it's reciprocal=1/x
given:
x+20=69*(1/x)
x(x+20)=69
 x^{2}+20x-69=0
solving the quadratic equation,
 x^{2}+23x-3x-69=0
x(x+23)-3(x+23)=0
(x-3)(x+23)=0
x=3 or x=-23
as x is whole number,x cannot be negative.
therefore,x=3

Answer 2

Answer:

The whole number  = 3

Step-by-step explanation:

Let 'x' be the whole number and the reciprocal of the number = $\frac{1}{x}$

The whole number increased by 20 = x+20

69 times the reciprocal of the number = 69×$\frac{1}{x}$

Given, The whole number increased by 20 = 69 times the reciprocal of the number

x+20 =  69×$\frac{1}{x}$

x(x+20) = 69

x² +20x - 69 = 0

x² +23x - 3x - 69 = 0

x(x+23) - 3(x+23) = 0

(x+23)(x-3) = 0

x =-23 or x= 3

Since 'x' is a whole number, x = -23 is not possible value of 'x'

∴ x = 3

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