Question

By how much $p+2q+3r$ should be increased to get $5q$?

• A. $3q-3p-3r$
  
• B. $3q+p-3r$
  
• C. $3q-p-3r$
• D. $q-p-3r$
  

Answer 1

The correct option is C $3q-p-3r$

Let the amount by which $p+2q+3r$ should be increased to get $5q$ be $x$.

Now, according to the question the sum of $p+2q+3r$ and $x$ should be equal to $5q$.

$\Rightarrow (p+2q+3r)+x=5q$
Subtracting $p+2q+3r$ from both sides of the above equation:

$\Rightarrow x=5q-(p+2q+3r)$

By removing the brackets, we get,

$\Rightarrow x=5q-p-2q-3r$

$\Rightarrow x=5q-(p+2q+3r)$
Combining the like terms in the RHS:

$\Rightarrow x=\underset{–}{(5q-2q)}-p-3r$
Subtracting the like terms:

$\Rightarrow x=3q-p-3r$

As a result, $p+2q+3r$ should be increased by $3q-p-3r$ to get $5q$.

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