Question

A positive number is 3 times another number. If 3 is added to the smallest number the difference between new number and greater become 31. What are the numbers

Answer 1

$\mathbf{Let \: \: numbers \: \: are \: \: x \: \: and \: \: 3x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [ \: \: According \: \: to \: \: the \: \: question \: ] \: \: }$


$\text{ Given, \: \: If \: 3 \: is \: added \: to \: smallest \: ( i.e. \: x ), \: difference \: between \: the \: greater \: number \: and \: new \: number \: becomes \: 31}$



According to the question :

=> 3x - ( x + 3 ) = 31

=> 3x - x - 3 = 31

=> 2x = 31 + 3

=> 2x = 34


$=> x = \frac{34}{2}$


$\bold{ = > \: x = 17}$




Hence, Numbers are :

x = 17
3x = 3( 17 ) = 51






Numbers : 17 and 51

Answer 2

Let the numbers be x and y.

Given that a positive number is 3 times another number .

= > x = 3y ------ (1)

Given that if 3 is added to the smallest number.

= > y + 3

The difference between new number and greater become 31.

= > x - (y + 3) = 31 ------ (2)

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Substitute (1) in (2), we get

= > 3y - (y + 3) = 31

= > 3y - y - 3 = 31

= > 2y = 34

= > y = 17

Substitute y = 17 in (1), we get

= > x = 3y

= > x = 3(17)

= > x = 51.

Therefore, the numbers are 17 and 51.

Hope this helps!