1Cademy - Solving a Two-Consecutive-Integer Sum Problem

Learn Before

Consecutive Integers

Example

Solving a Two-Consecutive-Integer Sum Problem

Apply the seven-step problem-solving strategy to find two consecutive integers when their sum is known.

Problem: The sum of two consecutive integers is $47$ . Find the numbers.

Read the problem.
Identify what to find: two consecutive integers.
Name the unknowns using the consecutive-integer pattern: Let $n$ = the first integer. Then $n + 1$ = the next consecutive integer.
Translate into an equation: The sum of the two integers equals $47$ , so:

$n + (n + 1) = 47$

Solve the equation. First, combine the like terms $n + n = 2n$ :

$2n + 1 = 47$

Subtract $1$ from both sides:

$2n = 46$

Divide both sides by $2$ :

$n = 23$

Find the second integer: $n + 1 = 23 + 1 = 24$ .

Check: $23 + 24 \stackrel{?}{=} 47$ → $47 = 47$ $\checkmark$
Answer: The two consecutive integers are $23$ and $24$ .

Because consecutive integers differ by exactly $1$ , the relationship between the unknowns is built into their algebraic representation ( $n$ and $n + 1$ ). This means the problem provides only one additional fact — the sum — which immediately yields a single-variable equation. Combining $n + n$ into $2n$ is the key simplification step before standard inverse operations isolate the variable.

Updated 2026-04-21

Contributors are:

Who are from:

References

OpenStax Elementary Algebra

Learn Before

Related

Learn After