Use a Problem-Solving Strategy: example 3.10

Find three consecutive even integers whose sum is 84.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find three consecutive even integers whose sum is 102.

How did it go?

Find three consecutive even integers whose sum is 84.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find three consecutive even integers whose sum is 102.

How did it go?

Step 1. Read the problem.
Step 2. Identify what we are looking for.	three consecutive even integers
Step 3. Name the integers.	Let $n = 1^{st}$ even integer. $n + 2 = 2^{nd}$ consecutive even integer $n + 4 = 3^{rd}$ consecutive even integer
Step 4. Translate.
Restate as one sentence.	The sume of the three even integers is 84.
Translate into an equation.	$n + n + 2 + n + 4 = 84$
Step 5. Solve the equation.
Combine like terms.	$n + n + 2 + n + 4 = 84$
Subtract 6 from each side.	$3 n + 6 = 84$
Divide each side by 3.	$3 n = 78$
	$\begin{matrix} n = 26 & 1^{st} integer \\ n + 2 & 2^{nd} integer \\ 26 + 2 \\ 28 \\ n + 4 & 3^{rd} integer \\ 26 + 4 \\ 30 \end{matrix}$
Step 6. Check.
$\begin{matrix} 26 + 28 + 30 \overset{?}{=} 84 \\ 84 = 84 ✓ \end{matrix}$
Step 7. Answer the question.	The three consecutive integers are 26, 28, and 30.

Step 1. Read the problem.
Step 2. Identify what we are looking for.	three consecutive even integers
Step 3. Name the integers.	Let $n = 1^{st}$ even integer. $n + 2 = 2^{nd}$ consecutive even integer $n + 4 = 3^{rd}$ consecutive even integer
Step 4. Translate.
Restate as one sentence.	The sume of the three even integers is 84.
Translate into an equation.	$n + n + 2 + n + 4 = 84$
Step 5. Solve the equation.
Combine like terms.	$n + n + 2 + n + 4 = 84$
Subtract 6 from each side.	$3 n + 6 = 84$
Divide each side by 3.	$3 n = 78$
	$\begin{matrix} n = 26 & 1^{st} integer \\ n + 2 & 2^{nd} integer \\ 26 + 2 \\ 28 \\ n + 4 & 3^{rd} integer \\ 26 + 4 \\ 30 \end{matrix}$
Step 6. Check.
$\begin{matrix} 26 + 28 + 30 \overset{?}{=} 84 \\ 84 = 84 ✓ \end{matrix}$
Step 7. Answer the question.	The three consecutive integers are 26, 28, and 30.