Question

The sum of three consecutive even numbers is 36. What are these numbers?

Answer 1

Answer:

Three consecutive integers whose sum is 36 are 10,12 , and 14 .

Step-by-step explanation:

Let 2n = the first even number, where n is an integer.

Let 2n + 2 = the second even number, and ...

Let 2n + 4 = the third even number.

With the above three equalities in mind, the statement that, "The sum of three consecutive even numbers is 36" can be translated mathematically into the following equation to be solved for n:

2n + (2n + 2) + (2n + 4) = 36

2n + 2n + 2 + 2n + 4 = 36

Collecting like-terms on the left, we have:

6n + 6 = 36

6n + 6 - 6 = 36 - 6

6n + 0 = 30

6n = 30

(6n)/6 = 30/6

(6/6)n = 5

(1)n = 5

n = 5

Therefore, ...

2n = 2(5) = 10

2n + 2 = 10 + 2 = 12

2n + 4 = 10 + 4 = 14

CHECK:

2n + (2n + 2) + (2n + 4) = 36

2(5) + (2(5) + 2) + (2(5) + 4) = 36

10 + 12 + 14 = 36

36 = 36

Therefore, the three consecutive even numbers are: 10, 12, and 14.

Answer 2

Given, the three numbers are consecutive even numbers

So let's take the numbers as '2x' , '2x+2' , '2x+4'

So

$</em><em>2</em><em>x + </em><em>2</em><em>x + </em><em>2</em><em> + </em><em>2</em><em>x + </em><em>4</em><em> = 36 \\ </em><em>6</em><em>x</em><em> </em><em>+</em><em> </em><em>6</em><em>= 36 \\ </em><em>6</em><em>x = 3</em><em>0</em><em> \\ x = </em><em>5</em><em>$

So 2x+2 = 2(5)+2 = 12

2x+4 = 2(5)+4 = 14

The three consecutive even numbers whose sum is 36 are 5,12 and 14