Equations, Inequalities, and Problem Solving

Solving Word Problems Involving Consecutive Even Integers

Word problems involving consecutive even integers are a common application of algebraic equations. The process involves translating a real-world scenario into an algebraic equation, solving for the unknown, and interpreting the result.

• Definition: Consecutive even integers are integers that follow one another in order and are each divisible by 2. For example, 26, 28, and 30.

• General Strategy: Use a variable to represent the first integer, then express the next consecutive even integers in terms of this variable.

Step 1: Understand the Problem

• Read and reread the problem to identify what is being asked.

• If x is the first even integer, the next consecutive even integer is x + 2, and the third is x + 4.

Step 2: Translate the Problem to an Equation

• In words: The sum of three consecutive even integers is 84.

• Translate:

Step 3: Solve the Equation

• Remove parentheses and combine like terms:

• Subtract 6 from both sides:

• Divide by 3:

Step 4: Interpret the Solution

• The first integer is 26.

• The second integer is 28 ().

• The third integer is 30 ().

Step 5: Check the Solution

• Add the three integers:

• Since the sum matches the original condition, the solution is correct.

Example

• Problem: Find three consecutive even integers whose sum is 84.

• Solution: The integers are 26, 28, and 30.

Additional info: This method can be generalized to solve for any set of consecutive even or odd integers by adjusting the increment (2 for even, 1 for odd).