# The sum of three consecutive even integers is 180. How do you find the numbers?

Mar 21, 2018

Answer: $58 , 60 , 62$

#### Explanation:

Sum of 3 consecutive even integers is 180; find the numbers.

We can start by letting the middle term be $2 n$ (note that we can't simply use $n$ since it would not guarantee even parity)

Since our middle term is $2 n$, our other two terms are $2 n - 2$ and $2 n + 2$. We can now write an equation for this problem!
$\left(2 n - 2\right) + \left(2 n\right) + \left(2 n + 2\right) = 180$

Simplifying, we have:
$6 n = 180$

So, $n = 30$

But we're not done yet. Since our terms are $2 n - 2 , 2 n , 2 n + 2$, we must substitute back in to find their values:
$2 n = 2 \cdot 30 = 60$
$2 n - 2 = 60 - 2 = 58$
$2 n + 2 = 60 + 2 = 62$

Therefore, the three consecutive even integers are $58 , 60 , 62$.

Mar 21, 2018

$58 , 60 , 62$

#### Explanation:

let the middle even numbe rbe $2 n$

the others will then be

$2 n - 2 \text{ and } 2 n + 2$

$\therefore 2 n - 2 + 2 n + 2 n + 2 = 180$

$\implies 6 n = 180$

$n = 30$

the numbers are

$2 n - 2 = 2 \times 30 - 2 = 58$

$2 n = 2 \times 30 = 60$

$2 n + 2 = 2 \times 30 + 2 = 62$

Mar 21, 2018

see a solution process below;

#### Explanation:

Let the three consecutive even integers be represented as; $x + 2 , x + 4 , \mathmr{and} x + 6$

Hence the sum of three consecutive even integers should be; $x + 2 + x + 4 + x + 6 = 180$

Therefore;

$x + 2 + x + 4 + x + 6 = 180$

$3 x + 12 = 180$

Subtract $12$ from both sides;

$3 x + 12 - 12 = 180 - 12$

$3 x = 168$

Divide both sides by $3$

$\frac{3 x}{3} = \frac{168}{3}$

$\frac{\cancel{3} x}{\cancel{3}} = \frac{168}{3}$

$x = 56$

Hence the three consecutive numbers are;

$x + 2 = 56 + 2 = 58$

$x + 4 = 56 + 4 = 60$

$x + 6 = 56 + 6 = 62$