Question #94595

Oct 3, 2016

$- 67$

Explanation:

Let the 3 consecutive integers be $- \left(x - 1\right) , - x , - \left(x + 1\right)$
$\implies - 204 = - \left(x - 1 + x + x + 1\right)$
$\implies - 204 = - 3 x$
$\implies 68 = x$

$\implies - \left(x - 1\right) = - \left(68 - 1\right) = - 67$
$- x = - 68$
$- \left(x + 1\right) = - \left(68 + 1\right) = - 69$

$\implies$ the largest of the3 consecutive integers $= - 67$

Oct 3, 2016

The three consecutive integers are $- 69. - 68 , - 67$
The largest is $- 67$

Explanation:

Let $x =$ the first integer.

The second consecutive integer is $x + 1$

The third consecutive integer is $x + 2$

If the sum of the three integers is $- 204$...

$x + x + 1 + x + 2 = - 204$

$3 x + 3 = - 204$

$\textcolor{w h i t e}{a a} - 3 \textcolor{w h i t e}{a a a a} - 3$

$\textcolor{w h i t e}{a a} 3 x \textcolor{w h i t e}{{a}^{1}} = - 207$

$\textcolor{w h i t e}{a} \frac{3 x}{3} \textcolor{w h i t e}{{a}^{1}} = - \frac{207}{3}$

$\textcolor{w h i t e}{{a}^{1}} x \textcolor{w h i t e}{a {a}^{1}} = - 69$

$x + 1 = - 68$

$x + 2 = - 67$

The three consecutive integers are $- 69. - 68 , - 67$

The largest is $- 67$