Question

Three consecutive integers add up to $51$. What are these integers?

• A. The three consecutive numbers are $10,14$ and $19$
• B. The three consecutive numbers are $13,15$ and $19$.
• C. The three consecutive numbers are $11,13$ and $15$.
• D. The three consecutive numbers are $16$, $17$ and $18$.

Answer 1

Answer: (D)

The three consecutive numbers are $16$, $17$ and $18$.

Let the three consecutive numbers be $x,(x+1)$ and $(x+2)$. Then,

$x+(x+1)+(x+2)=51$

$\Rightarrow 3x+3=51$
$\Rightarrow 3x=51-3=48$

$\Rightarrow x=\frac{48}{3}=16$

Hence, the three consecutive numbers are $16,17$ and $18$.