Question

Sum of three consecutive integers is $24$. Find product of the integers.

Answer 1

Let the three consecutive integers be $x,x+1$ and $x+2$.

It is given that the sum of the integers is $24$, therefore, we have:

$x+(x+1)+(x+2)=24\Rightarrow x+x+1+x+2=24\Rightarrow 3x+3=24\Rightarrow 3x=24-3\Rightarrow 3x=21\Rightarrow x=\frac{21}{3}\Rightarrow x=7$

Therefore, $x=7$ and the other two integers are:

$x+1=7+1=8$ and

$x+2=7+2=9$

Now, we find the product of the integers as shown below:

$x(x+1)(x+2)=7\times 8\times 9=504$

Hence, the product of the integers is $504$.