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.