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

Answer:

The smaller number can be 8 or $\frac{1}{5}$.

Step-by-step 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.

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

$6y+4=y+5$

$5y=1$

$y=\frac{1}{5}$

Therefore, the smaller number is $\frac{1}{5}$.