Question

Find the missing digits in the following additions.
$2222$
$+99$

$+9$

$\underset{–}{+AAA}$

$\underset{–}{299A}$

Answer 1

Since, a number can be written as the sum of the place value of all of its digit.
That is, we can write,
$AAA=100A+10A+A$
And, $299A=2000+900+90+A.$
Here, the given expression,
$2222+99+9+AAA=299A$
$\Rightarrow 2222+99+9+100A+10A+A=2000+900+90+A$
$\Rightarrow 2330+111A=2990+A$
$\Rightarrow 111A-A=2990-2230$
$\Rightarrow 110A=660$
$\Rightarrow A=6$
Hence, the value of $A$ is $6.$