Chapter 1.2, Problem 49E

To determine

To find the three consecutive even integers.

Answer to Problem 49E

16, 18 and 20

Explanation of Solution

Given:

Sum of three consecutive integers is 54.

Calculation:

Let, the three consecutive even integers be $(2n-2),2n$ and $2n+2$ where n is integer.

Now,

The sum of these integers is 54, which means,

  $\begin{array}{l}\Rightarrow 2n-2+2n+2n+2=54\\ \Rightarrow 6n=54\\ \Rightarrow n=\frac{54}{6}\\ \Rightarrow n=9\end{array}$

Conclusion:

Hence, the required consecutive even integers are:

  $(2n-2)=2\times 9-2=16$

  $(2n)=2\times 9=18$

  $(2n+2)=2\times 9+2=20$