Question

In each of the problems below the result of doing some operation on a number is given. Find the number?

1). $3$ added to double is $101.$

2). $2$ added to triple is $101.$

3). $3$ subtracted from double is $101.$

4). $2$ subtracted from triple is $101.$

Answer 1

Case $1)$ $3$ added to double is $101.$

which means when we add $3$ to a double number gives $101.$
let the number be $x.$
Mathematically it can be represented as
$\Rightarrow 3+2x=101$

$\Rightarrow 2x=101-3$

$\Rightarrow 2x=98$

$\Rightarrow x=\frac{98}{2}$

$\therefore x=49$

So, number is $49$
Case $2)$ $2$ added to triple is $101.$

Let the number is $y.$

Mathemattically, it can be written as

$\Rightarrow 2+3y=101$

$\Rightarrow 3y=101-2$

$\Rightarrow 3y=99$

$\therefore y=\frac{99}{3}=33$

Case $3)$ $3$ subtracted from double is $101.$

let the number is $z.$

It can be written as
$\Rightarrow 2z-3=101$

$\Rightarrow 2z=101+3$

$\Rightarrow 2z=104$

$z=\frac{104}{2}=52$

Case $4)$ $2$ subtracted from triple is $101.$

let the number is $p$

$\Rightarrow 3p-2=101$

$\Rightarrow 3p=101+2$

$\Rightarrow 3p=103$

$\therefore p=\frac{103}{3}$