Chapter 8.3, Problem 21HP

To determine

Find 3 consecutive even numbers whose sum is 30.

Answer to Problem 21HP

The 3 consecutive even numbers are $8,10,12$ whose sum is 30.

Explanation of Solution

Given:

Find 3 consecutive even numbers whose sum is 30.

Concept Used:

The difference between two consecutive even numbers is 2.

Let the 3 consecutive even numbers are $n,n+2,n+4$

Given the sum of 3 consecutive numbers is 30.

The required equation is: $n+n+2+n+4=30$

Calculation:

The required equation is: $n+n+2+n+4=30$

  $\begin{array}{l}3n+6=30\\ 3n+6-6=30-6\text{[}\text{Subtract 6 from both sides]}\\ 3n=24\\ \frac{3n}{3}=\frac{24}{3}[\text{Divide}\text{each}\text{side}\text{by}\text{3}]\\ n=8\end{array}$

The 3 consecutive even numbers are: $n=8;n+2=10;n+4=12;$

Thus, the 3 consecutive even numbers are $8,10,12$ whose sum is 30.