Math Problem Statement

find three every other even integers such that the sum of all three integers is equal to three times 

Solution

To find three every other even integers such that their sum is equal to three times something (though the exact multiplier is unclear), let's proceed with the following general approach:

Step-by-step process:

  1. Define the integers: Let the three every other even integers be: x,x+4,x+8x, \quad x + 4, \quad x + 8 where xx is the first even integer, x+4x + 4 is the next even integer, and x+8x + 8 is the third even integer.

  2. Sum of the integers: The sum of these three integers is: x+(x+4)+(x+8)=3x+12x + (x + 4) + (x + 8) = 3x + 12

  3. Relating to three times a number: If the sum is supposed to be three times a certain number, say kk, then we set up the equation: 3x+12=3k3x + 12 = 3k

  4. Solve for xx: To find xx, divide both sides of the equation by 3: x+4=kx + 4 = k x=k4x = k - 4

  5. Conclusion: The three every other even integers are: (k4),(k),(k+4)(k - 4), \quad (k), \quad (k + 4) So, the solution depends on what kk is.

Missing information:

If you know the value of kk, I can calculate the integers for you.

Would you like to clarify the value for kk, or do you have any questions?


Follow-up questions:

  1. What is the value of kk in this case?
  2. Would you like to solve this problem with specific values of kk?
  3. Do you need help with another type of integer progression?
  4. Are you interested in exploring odd integers instead?
  5. Would you like to see the step-by-step solution for similar problems?

Tip: When dealing with arithmetic progressions, try to generalize the relation between consecutive terms to simplify your calculations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Arithmetic Progressions
Linear Equations

Formulas

Sum of three integers: x + (x + 4) + (x + 8) = 3x + 12
Relating the sum to a multiplier: 3x + 12 = 3k

Theorems

Linear Equation Solving

Suitable Grade Level

Grades 6-8