Question 427596
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(a) when I open a book two page face me, the sum of the page number is 85. what are the page number ? 
(b) if the sum is not give, but the product is gives to be 1806, how will your find the page number
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                Part  (a)


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Let the page numbers are n and (n+1), two consecutive integer numbers.

The problem says that

    n + (n+1) = 85.


Simplify and find 'n'

    2n + 1 = 85,

    2n = 85 - n1 = 84,

     n =           84/2 = 42.


<U>ANWER</U>.  The pages are '42' and '43'.
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Part &nbsp;(b)


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This time, the equation is

    n*(n+1) = 1806.


You can solve it by guessing n = 42 or by advanced guessing with reasoning.


Alternatively, you can reduce it to quadratic equation

    n^2 + n - 1806 = 0

and solve it using the quadratic formula or factoring.


Or you can evaluate the square root of 1806:  {{{sqrt(1806)}}} = 42.497 approximately, 
which tells you that n = 42.
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Thus, &nbsp;both parts, &nbsp;(a) &nbsp;and &nbsp;(b), &nbsp;are solved.