Question

Write an expression for the following.
the sum of 3 consecutive even integers is 36

Answer 1

Answer:

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

Answer 2

Answer:

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.

Step-by-step explanation: