Question

Sum of two consecutive even natural number is 24 this statement can be represented by the equations x + (2x + 2) = 24 ​

Answer 1

Answer:

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

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

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

Since the sum of the three unknown consecutive even numbers is 24, we can write the following equation to be solved for n as follows:

2n + (2n + 2) + (2n + 4) = 24

2n + 2n + 2 + 2n + 4 = 24

2n + 2n + 2n + 2 + 4 = 24

Collecting like-terms on the left, we get:

6n + 6 = 24

6n + 6 - 6 = 24 - 6

6n + 0 = 18

6n = 18

(6n)/6 = 18/6

(6/6)n = 18/6

(1)n = 3

n = 3

Therefore, ...

2n = 2(3) = 6 and

2n + 2 = 6 + 2 = 8 and

2n + 4 = 6 + 4 = 10

CHECK:

2n + (2n + 2) + (2n + 4) = 24

6 + (8) + (10) = 24

6 + 8 + 10 = 24

14 + 10 = 24

24 = 24

Therefore, the three desired consecutive even numbers whose sum is 24 are indeed 6, 8, and 10, and the median or middle value is plainly 8.