What is the greatest of 5 consecutive integers if the sum of these integers equals 185?

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Answer 1 · 2017-02-04T04:19:34

39 is the greatest of the 5 consecutive integers adding to 185.

First, let's define the 5 consecutive integers.

We can call the smallest of the 5 consecutive integers $x$ $x$ .

Then, by definition of "consecutive integers" the remaining 4 would be:

$x + 1$ $x + 1$ , $x + 2$ $x + 2$ , $x + 3$ $x + 3$ and $x + 4$ $x + 4$

The sum of these 5 consecutive integers equals 185 so we can write and solve for $x$ $x$ :

$x + x + 1 + x + 2 + x + 3 + x + 4 = 185$ $x + x + 1 + x + 2 + x + 3 + x + 4 = 185$

$5 x + 10 = 185$ $5x + 10 = 185$

$5 x + 10 - 10 = 185 - 10$ $5x + 10 - color(red)(10) = 185 - color(red)(10)$

$5 x + 0 = 175$ $5x + 0 = 175$

$5 x = 175$ $5x = 175$

$\frac{5 x}{5} = \frac{175}{5}$ $(5x)/color(red)(5) = 175/color(red)(5)$

$(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 35$

$x = 35$

We are looking for the greatest of the 5 consecutive integers or $x + 4 -> 35 + 4 = 39$