The sum of four consecutive integers is 2174. How do you find the numbers?

Apr 27, 2018

You can take the 1st integer as $x$ and other consecutive integers as $x + 1 , x + 2 , x + 3$

Sum up and find the value of $x$, then we get the values of the other integers.

Explanation:

Let the 1st integer be $x$, next consecutive integers will be (x+1), (x+2) and (x+3).

Now,
$x + \left(x + 1\right) + \left(x + 2\right) + \left(x + 3\right) = 2174$

or,$4 x + 6 = 2174$

or, $4 x = 2174 - 6$

or, $4 x = 2168$

or, $x = \frac{2168}{4}$

or, $x = 542$

So,
$x + 1 = 543$

$x + 2 = 544$

$x + 3 = 545$

The four consecutive integers are $542 , 543 , 544 , 545.$

Apr 27, 2018

Four consecutive integers :$542 , 543 , 544 , 545.$

Explanation:

Let the four consecutive integers:

$n , n + 1 , n + 2 , n + 3.$

Given that,

Sum=2174,

$\implies n + \left(n + 1\right) + \left(n + 2\right) + \left(n + 3\right) = 2174$

$\implies 4 n + 6 = 2174$

$\implies 4 n = 2168$

$\implies n = 542$

So,

$n + 1 = 542 + 1 = 543$

$n + 2 = 542 + 2 = 544$

$n + 3 = 542 + 3 = 545$

Hence, four consecutive integers :$542 , 543 , 544 , 545.$

Apr 27, 2018

The numbers are $\text{ "542," "543," "544," } 545$

Explanation:

Consecutive numbers are those that follow each other like 17,18,19,... They differ by $1$.

Let the numbers be $\text{ "x," "x+1," "x+2," } x + 3$

Their sum is $2174$

$x + x + 1 + x + 2 + x + 3 = 2174$

$4 x + 6 = 2174$

$4 x = 2174 - 6$

$4 x = 2168$

$x = 542$

The first number is $542.$

The numbers are $\text{ "542," "543," "544," } 545$