Answer
The greatest integer of the four consecutive integers is $64$.
Work Step by Step
We have to define our variable.
Let $x$ = the lowest number of a set of consecutive integers
Let $x + 1$, $x + 2$, and $x + 3$ be three integers that are consecutive to $x$.
Let's set up the equation to find the integers:
$x + (x + 1) + (x + 2) + (x + 3) = 250$
Combine like terms:
$4x + 6 = 250$
Collect all constant terms on the right side of the equation by subtracting $6$ from each side of the equation:
$4x = 244$
Divide each side of the equation by $4$ to solve for $x$:
$x = 61$
We want the greatest integer, which can be found by solving the expression $x + 3$, which would be the fourth and largest integer among the four numbers:
$x + 3$
Substitute $61$ for $x$ in the expression:
$61 + 3$
Add to solve:
The greatest integer of the four consecutive integers is $64$.
