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A set of 33 consecutive integers adds up to 2727. Which integers are they?\newline_\_, _\_, _\_

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Full solution

Q. A set of 33 consecutive integers adds up to 2727. Which integers are they?\newline_\_, _\_, _\_
  1. Denote First Integer: Let's denote the first integer as xx. Since we are looking for consecutive integers, the next two integers will be x+1x+1 and x+2x+2.
  2. Write Equation: The sum of these three consecutive integers is given as 2727. Therefore, we can write the equation as x+(x+1)+(x+2)=27x + (x+1) + (x+2) = 27.
  3. Simplify Equation: Simplify the equation by combining like terms: x+x+x+1+2=27x + x + x + 1 + 2 = 27 which simplifies to 3x+3=273x + 3 = 27.
  4. Isolate Variable: Subtract 33 from both sides of the equation to isolate the term with the variable: 3x+3−3=27−33x + 3 - 3 = 27 - 3 which simplifies to 3x=243x = 24.
  5. Solve for x: Divide both sides of the equation by 33 to solve for x: 3x3=243\frac{3x}{3} = \frac{24}{3} which simplifies to x=8x = 8.
  6. Find Consecutive Integers: Now that we have the value of xx, we can find the three consecutive integers. The first integer is x=8x = 8, the second integer is x+1=8+1=9x + 1 = 8 + 1 = 9, and the third integer is x+2=8+2=10x + 2 = 8 + 2 = 10.

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