Math Problem Statement

Find three consecutive integers with a sum of 93.

Solution

The problem asks to find three consecutive integers that sum up to 93.

Let the three consecutive integers be:

  • xx (the first integer),
  • x+1x+1 (the second integer),
  • x+2x+2 (the third integer).

The sum of these three integers is given by:

x+(x+1)+(x+2)=93x + (x + 1) + (x + 2) = 93

Simplifying:

3x+3=933x + 3 = 93

Now, subtract 3 from both sides:

3x=903x = 90

Next, divide by 3:

x=30x = 30

Thus, the three consecutive integers are:

30,31,3230, 31, 32

Do you want more details or have any questions?

Here are some related questions you might find interesting:

  1. What if the sum were 99 instead of 93? How would the integers change?
  2. How do we handle finding four consecutive integers with a given sum?
  3. How can we solve for consecutive even integers with a given sum?
  4. How do we generalize this approach for any number of consecutive integers?
  5. How do we solve the same problem if the integers are consecutive odd numbers?

Tip: When solving problems involving consecutive integers, always set up the variables so that their sum can be easily simplified (like using x,x+1,x+2x, x+1, x+2 for three consecutive numbers).

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Math Problem Analysis

Mathematical Concepts

Algebra
Consecutive Integers

Formulas

x + (x + 1) + (x + 2) = 93

Theorems

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Suitable Grade Level

Grades 6-8