Answer:
Let 2n = the first of three consecutive even numbers, where n is an integer.
Let 2n + 2 = the second of three consecutive even numbers, and
Let 2n + 4 = the third of three consecutive even numbers.
We're given that "sum of three consecutive even numbers is 552." We can translate this English sentence mathematically into the following equation to be solved for n:
2n + (2n + 2) + (2n + 4) = 552
Removing the parentheses, we have:
2n + 2n + 2 + 2n + 4 = 552
Now, by the Commutative Law of Addition, i.e., a + b = b + a, we have on the left side of the equation:
2n + 2n + 2n + 2 + 4 = 552
Now, collecting like-terms on the left, we get:
6n + 6 = 552
To solve for the variable n, We now begin isolating n on the left side by subtracting 6 from both sides as follows:
6n + 6 - 6 = 552 - 6
6n + 0 = 546
6n = 546
Now, divide both sides by 6 to finally solve for n:
(6n)/6 = 546/6
(6/6)n = 546/6
(1)n = 91
n = 91
Therefore, the first of three consecutive even numbers, 2n, is:
2n = 2(91)
= 182
The second of three consecutive even numbers is:
2n + 2 = 2(91) + 2
= 182 + 2
= 184
The third of three consecutive even numbers is:
2n + 4 = 2(91) + 4
= 182 + 4
= 186
CHECK:
2n + (2n + 2) + (2n + 4) = 552
182 + 184 + 186 = 552
552 = 552
Therefore, the desired and first of three consecutive even numbers is indeed 2n = 182.
