Question

x, y are natural numbers such that x > y. Also x + y + xy = 80, then value of x is

Answer 1

X and Y are natural numbers such that X > Y.

We have X + Y + X*Y = 80

           or, Y + X*( 1 + Y) = 80

           or, X*( 1 + Y) = 80 - Y

           or, X = (80 - Y) / (1 + Y)

Since Y is a natural number, we count from 1 for the value of Y until we get X > Y

          Value of Y                   Value of X                             decision

                 1                                    39.5                                    X

                 2                                    26                               ACCEPTED

                 3                                    77/4                                   X

                 4                                    76/5                                  X

                 5                                    75/6                                  X

                 6                                    74/7                                  X

                 7                                     73/8                                 X

                8                                        8                            ACCEPTED

                9                                       7.1                                   X

From 9, we have greater value of Y than X which can not be taken.

So, from the table, we have X = 8 or 26 while the values of Y is 8 and 2 respectively.(ans.)

Answer 2

Given:

x and y are natural numbers.

Natural numbers: 1,2,3,...

Condition:

x>y

x+y+xy=80

Deductions:

If x=2, then y<2.

In order to satisfy the second condition,

Consider,

x=26

y=2

Condition 1 is satisfied because 26<1

26+2+(26*2)=80

28+52=80

Hence, Condition 2 is also satisfied.

Therefore,

x=26 and y=2.

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