Chapter 4.6, Problem 21HP

To determine

To find: three consecutive even numbers

Answer to Problem 21HP

The required three consecutive even numbers are 8, 10, and 12.

Explanation of Solution

Given:

Sum of consecutive even numbers =30

Calculation:

An example of two consecutive even numbers is 4 and 6. They can be represented by n and n+2.

Combining all conditions together,

  $\begin{array}{l}n+n+2+n+4=30\\ 3n+2+4=30\text{ Distributive property}\\ 3n+2+4-2-4=30-2-4\text{ Subtraction property of equality}\\ 3n=24\text{ Simplify}\\ \frac{3n}{3}=\frac{24}{3}\text{ Divide by 3 on both sides}\\ n=8\end{array}$

Find the remaining two numbers

  $\begin{array}{l}n=8\\ n+2=8+2=10\\ n+4=8+4=12\end{array}$

Hence, the required three consecutive even numbers are 8, 10 and 12.

Conclusion:

Hence, the required three consecutive even numbers are 8, 10 and 12.