Question

A positive number is 3 times another number.

If we add 2 to the larger and 5 to the smaller, then one of them becomes 2 times the other.
Find the smaller number.​

Answer 1

The smaller number can be 8 or
`(1)/(5)`.

Explanation:

Consider the provided information.

let the larger number is x and the smaller number is y

A positive number is 3 times another number.

`3y=x`

If we add 2 to the larger and 5 to the smaller, then one of them becomes 2 times the other.

Case I: If 2nd number is 2 times to the first number.

`x+2=2(y+5)`

Substitute the value of x.

`3y+2=2y+10`

`y=8`

Now substitute the value of y in
`3y=x`

`3(8)=x`

`x=24`

Therefore, the smaller number is 8.

Case II: If 1st number is 2 times to the second number.

`2(x+2)=y+5`

Substitute the value of x.

`2(3y+2)=y+5`

`6y+4=y+5`

`5y=1`

`y=(1)/(5)`

Therefore, the smaller number is
`(1)/(5)`.