Question

John finds that the sum of two numbers is 24 and their difference is one sixth of the

sum. Find the smallest number between the two numbers.

Answer 1

Given:

The sum of two numbers is 24 and their difference is one sixth of the sum.

To find:

The smaller number between the two numbers.

Solution:

Let x and y be the two numbers where x>y.

The sum of two numbers is 24.

`x+y=24` ...(i)

Their difference is one sixth of the sum.

`x-y=(1)/(6)* 24`

`x-y=4` ...(ii)

Adding (i) and (ii), we get

`2x=28`

`x=(28)/(2)`

`x=14`

Putting
`x=14` in (i), we get

`14+y=24`

`y=24-14`

`y=10`

The two numbers are 14 and 10.

Therefore, the smaller number between the two numbers is 10.