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The sum of three consecutive integers is 81 . Find the value of the greatest of the three. Answer:

The sum of three consecutive integers is 8181 . Find the value of the greatest of the three.\newlineAnswer:

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Full solution

Q. The sum of three consecutive integers is 8181 . Find the value of the greatest of the three.\newlineAnswer:
  1. Denote first integer as xx: Let's denote the first integer as xx. Since we are dealing with consecutive integers, the next two integers will be x+1x+1 and x+2x+2.
  2. Write sum equation: The sum of these three consecutive integers is given as 8181. Therefore, we can write the equation as x+(x+1)+(x+2)=81x + (x+1) + (x+2) = 81.
  3. Simplify equation: Simplify the equation by combining like terms: x+x+x+1+2=81x + x + x + 1 + 2 = 81 which simplifies to 3x+3=813x + 3 = 81.
  4. Isolate variable term: Subtract 33 from both sides of the equation to isolate the term with the variable: 3x+3−3=81−33x + 3 - 3 = 81 - 3 which simplifies to 3x=783x = 78.
  5. Solve for x: Divide both sides of the equation by 33 to solve for x: 3x3=783\frac{3x}{3} = \frac{78}{3} which simplifies to x=26x = 26.
  6. Find greatest integer: Now that we have the value of the first integer, x=26x = 26, we can find the greatest of the three consecutive integers by adding 22 to xx: 26+2=2826 + 2 = 28.

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