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A set of 33 consecutive integers adds up to 4242. What are the integers?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_

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Q. A set of 33 consecutive integers adds up to 4242. What are the integers?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_
  1. Define Integers: Let xx be the first integer. The three consecutive integers can be represented as xx, x+1x+1, and x+2x+2.
  2. Set Up Equation: Set up the equation to represent the sum of the three consecutive integers equal to 4242: x+(x+1)+(x+2)=42x + (x+1) + (x+2) = 42.
  3. Simplify Equation: Simplify the equation: x+x+1+x+2=42x + x + 1 + x + 2 = 42. Combine like terms: 3x+3=423x + 3 = 42.
  4. Isolate Variable Term: Isolate the variable term by subtracting 33 from both sides of the equation: 3x+3−3=42−33x + 3 - 3 = 42 - 3. This simplifies to 3x=393x = 39.
  5. Divide to Solve: Divide both sides of the equation by 33 to solve for xx: 3x3=393\frac{3x}{3} = \frac{39}{3}. This gives us x=13x = 13.
  6. Find Consecutive Integers: Now that we have the value of xx, we can find the three consecutive integers: xx, x+1x+1, and x+2x+2. Substitute xx with 1313: 1313, 13+113+1, 13+213+2. This gives us the integers 1313, xx00, xx11.

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