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,
[tex]12r+\dfrac{1}{2}s=17[/tex] ...(i)
Twice the number r plus one-twelfth of the number s equals seven.
[tex]2r+\dfrac{1}{12}s=7[/tex] ...(ii)
Multiply both sides by 2 in (i).
[tex]24r+s=34[/tex] ...(iii)
Multiply both sides by 12 in (ii).
[tex]24r+s=84[/tex] ...(iv)
Using (iii) and (iv), we get
[tex]43=84[/tex], which is a false statement because [tex]43\neq 84[/tex].
It means, equation (i) and (ii) has not solutions.
Therefore, the two numbers for the given problem does not exist.
