Question

What algebraic expression must be added to $9y$ to get $25x?$

• A. $16y$
• B. $16x$
• C. $25x-9y$
• D. $25y-9x$

Answer 1

The correct option is C $25x-9y$

Let the algebraic expression added to $9y$ be $a$.

Now, according to the question, the sum obtained is equal to $25x$, i.e.,
$9y+a=25x$
subtracting $9y$ from both sides,

$\Rightarrow 9y+a-9y=25x-9y$

$\Rightarrow a=25x-9y$

$\therefore$ We need to add $\underset{–}{25x-9y}$ to $\underset{–}{9y}$ to get the value of the sum as $\underset{–}{25x}.$

Therefore, option (c.) is the correct answer.

$\underset{–}{\text{Verification:}}$

Adding $25x-9y$ and $9y$ should give $25x$, i.e.,
$\Rightarrow (25x-9y)+9y=25x$
$\Rightarrow 25x+(9y-9y)=25x$
$\Rightarrow 25x=25x$
L.H.S $=$ R.H.S
Hence, verified.