Math Problem Statement

The sum of three consecutive integers is 174. What are the​ integers?

Solution

Let the three consecutive integers be nn, n+1n+1, and n+2n+2.

The sum of these integers can be expressed as:

n+(n+1)+(n+2)=174n + (n+1) + (n+2) = 174

Simplifying the equation:

3n+3=1743n + 3 = 174

Subtract 3 from both sides:

3n=1713n = 171

Divide both sides by 3:

n=57n = 57

So, the three consecutive integers are:

57,58, and 5957, 58, \text{ and } 59

Would you like more details or have any questions?

Here are some related questions:

  1. What if the sum of four consecutive integers is 174?
  2. How would the solution change if the integers were consecutive even numbers?
  3. What are the three consecutive integers if their sum is 201?
  4. How can you express the sum of any three consecutive integers in a general form?
  5. What is the product of the three consecutive integers found?

Tip: When solving for consecutive integers, always express them in terms of a single variable to simplify the equation.

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Math Problem Analysis

Mathematical Concepts

Integer Arithmetic
Linear Equations

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9