Question

Find the 3 consecutive even numbers whose sum is 18.


solve the problem ​

Answer 1

Answer:

4,6,8

Step-by-step explanation:

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

Let 2n + 2 = the second consecutive even integer, and ...

Let 2n + 4 = the third consecutive even integer.

Since the sum of the three consecutive even integers is 18, then we can write the following equation to be solved for n:

2n + (2n + 2) + (2n + 4) = 18

2n + 2n + 2 + 2n + 4 = 18

Now, collecting like-terms, we get:

6n + 6 = 18

6n + 6 - 6 = 18 - 6

6n + 0 = 12

6n = 12

(6n)/6 = 12/6

(6/6)n = 12/6

(1)n = 2

n = 2

Therefore, ...

2n = 2(2) = 4

2n + 2 = 4 + 2 = 6

2n + 4 = 4 + 4 = 8

CHECK:

2n + (2n + 2) + (2n + 4) = 18

4 + (6) + (8) = 18

4 + 6 + 8 = 18

10 + 8 = 18

18 = 18

Therefore, our desired consecutive even integers whose sum is 18 are indeed 4, 6, and 8.

Answer 2

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