Math Problem Statement

Three consecutive integers add up to 252. What are the integers?

Solution

The question asks for three consecutive integers whose sum is 252. Let's solve this step-by-step:

Let the three consecutive integers be:

  • xx (the smallest integer),
  • x+1x+1 (the next consecutive integer),
  • x+2x+2 (the largest consecutive integer).

Step 1: Write the equation

The sum of these three integers is: x+(x+1)+(x+2)=252x + (x+1) + (x+2) = 252

Step 2: Simplify the equation

Combine like terms: 3x+3=2523x + 3 = 252

Step 3: Solve for xx

Subtract 3 from both sides: 3x=2493x = 249

Divide by 3: x=83x = 83

Step 4: Find the integers

The three integers are:

  • x=83x = 83,
  • x+1=84x+1 = 84,
  • x+2=85x+2 = 85.

Final Answer:

The integers are 83, 84, and 85.

Would you like a detailed explanation or have any questions?


Here are 5 related questions to expand your understanding:

  1. How would the solution change if the sum were 300 instead of 252?
  2. Can you solve for four consecutive integers adding up to a specific number?
  3. How can you write an equation for consecutive even integers?
  4. What happens if one of the integers is missing from the sum? How do you solve it?
  5. What is the relationship between the average of the integers and their sum?

Tip: For problems involving consecutive numbers, remember to use algebraic expressions like x,x+1,x+2x, x+1, x+2, etc., to simplify the solution process.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Consecutive Integers

Formulas

Sum of three consecutive integers: x + (x+1) + (x+2)

Theorems

Basic principles of solving linear equations

Suitable Grade Level

Grade 6-8