Question

A set of 4 consecutive integers adds up to 310. What is the value of the greatest integer?

Answer 1

We can define the 4 consecutive integers as n, n+1, n+2 and n+3.

The index n is a integer value.

We know that if we add them, we get 310.

Then, we can write:

$\begin{gathered} n+(n+1)+(n+2)+(n+3)=310 \\ 4n+6=310 \\ 4n=310-6 \\ 4n=304 \\ n=\frac{304}{4} \\ n=76 \end{gathered}$

Now that we know the value of n (n=76), we can calculate the value of our greatest integer, which has a value of n+3:

$n+3=76+3=79$

Answer: the greatest integer of the list is 79.

To verify, we can do:

$76+77+78+79=310$