Question

REASONING An even integer can be represented by the expression $2n$ , where $n$ is any integer. Find three consecutive even integers that have a sum of 54. The three consecutive even integers, in order from least to greatest, are , , and . Explain your reasoning. Expressions for the next two consecutive even integers after $2n$ are and . Solving the equation $=54$ , and substituting the solution into the expressions for the three integers results in the three integers given above.

Answer 1

First Integer = 16

Second Integer = 18

Third integer = 20

Explanation:

An even integer is represented by 2n

Where n is any integer

Let :

First Integer = 2n - 2

Second Integer = 2n

Third integer = 2n + 2

The sum of three even consecutive numbers = 2n - 2 + 2n + 2n + 2

= 2n + 2n + 2n - 2 + 2 = 54

= 6n = 54

n = 54/6

n = 9

First Integer = 2n - 2 = 2(9) - 2

= 16

Second Integer = 2n = 2(9)

= 18

Third integer = 2n + 2 = 2(9) + 2

= 20