Question

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?​

Answer 1

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,

`12r+(1)/(2)s=17` ...(i)

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

`2r+(1)/(12)s=7` ...(ii)

Multiply both sides by 2 in (i).

`24r+s=34` ...(iii)

Multiply both sides by 12 in (ii).

`24r+s=84` ...(iv)

Using (iii) and (iv), we get

`43=84`, which is a false statement because
`43\\eq 84`.

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

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