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There are 33 consecutive integers with a sum of 99. What are the integers?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_

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Q. There are 33 consecutive integers with a sum of 99. What are the integers?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_
  1. Define Integers: Let xx be the first integer.\newlineWhich represents the three consecutive integers?\newlineConsecutive integers increase by 11 each time.\newlineConsecutive integers: xx, x+1x+1, x+2x+2
  2. Sum of Consecutive Integers: Which equation represents the sum of 33 consecutive integers is 99?\newlineAdd three consecutive integers and equate the sum to 99.\newlineEquation: x+(x+1)+(x+2)=9x + (x+1) + (x+2) = 9
  3. Simplify Equation: Simplify the left side of x+(x+1)+(x+2)=9x + (x+1) + (x+2) = 9.\newlinex+(x+1)+(x+2)=9x + (x+1) + (x+2) = 9\newline(x+x+x)+(1+2)=9(x + x + x) + (1+2) = 9\newline3x+3=93x + 3 = 9
  4. Isolate Variable Term: Isolate the variable term in 3x+3=93x + 3 = 9.
    3x+3=93x + 3 = 9
    3x+3−3=9−33x + 3 - 3 = 9 - 3
    3x=63x = 6
  5. Solve for x: 3x=63x = 6\newlineSolve for x.\newline3x=63x = 6\newline(3x)/3=6/3(3x)/3 = 6/3\newlinex=2x = 2
  6. Identify Consecutive Integers: We have:\newlinex=2x = 2\newlineWhat are the 33 consecutive integers that add up to 99?\newlineThree consecutive integers:\newlinex,x+1,x+2x, x+1, x+2\newline2,2+1,2+22, 2+1, 2+2\newline2,3,42, 3, 4

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