Twelve times a number r plus half a number s equals seventeen. Twice the number r plus one-twelfth of the number s equals seven. What are the two numbers?

Given:

Twelve times a number r plus half a number s equals seventeen.

Twice the number r plus  one-twelfth of the number s equals seven.

To find:

The two numbers.

Solution:

Twelve times a number r plus half a number s equals seventeen. So,

     ...(i)

Twice the number r plus  one-twelfth of the number s equals seven.

         ...(ii)

Multiply both sides by 2 in (i).

        ...(iii)

Multiply both sides by 12 in (ii).

       ...(iv)

Using (iii) and (iv), we get

, which is a false statement because .

It means, equation (i) and (ii) has not solutions.

Therefore, the two numbers for the given problem does not exist.