Chapter 1.2, Problem 49E

To determine

To find: three consecutive even integers.

Answer to Problem 49E

Three consecutive even integers are $\text{16, 18, 20}$

Explanation of Solution

Given:

Expression $2n$

Calculation:

1st Integer: $2n-2$ 2nd Integer: $2n$ 3rd Integer: $2n+2$	Define variables. The middle even integer is equal to $2n$ , the 1st integer is 2 less than the middle eveninteger and the 3rd integer is 2 more than the middle even integer.
$\left(2n-2\right)+2n+\left(2n+2\right)=54$	The sum of the integers is 54.
$6n=54$	Combine like terms.
$n=9$	.Divide both sides by 6.
$\begin{array}{l}2n-2=2\left(9\right)-2=18-2=16\\ 2n=2\left(9\right)=18\\ 2n+2=2\left(9\right)+2=18+2=20\end{array}$	Use the value of n to find the value of each integer

  $\text{16, 18, 20}$

Conclusion:

Three consecutive even integers are $\text{16, 18, 20}$