Math Problem Statement
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:
- (the smallest integer),
- (the next consecutive integer),
- (the largest consecutive integer).
Step 1: Write the equation
The sum of these three integers is:
Step 2: Simplify the equation
Combine like terms:
Step 3: Solve for
Subtract 3 from both sides:
Divide by 3:
Step 4: Find the integers
The three integers are:
- ,
- ,
- .
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:
- How would the solution change if the sum were 300 instead of 252?
- Can you solve for four consecutive integers adding up to a specific number?
- How can you write an equation for consecutive even integers?
- What happens if one of the integers is missing from the sum? How do you solve it?
- 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 , 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
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