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There are 33 consecutive integers with a sum of 5151. What are the integers?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_

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Q. There are 33 consecutive integers with a sum of 5151. What are the integers?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_
  1. Identify First Integer: 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 5151?\newlineAdd three consecutive integers and equate the sum to 5151.\newlineEquation: x+(x+1)+(x+2)=51x + (x+1) + (x+2) = 51
  3. Simplify Equation: Simplify the left side of x+(x+1)+(x+2)=51x + (x+1) + (x+2) = 51.\newlinex+(x+1)+(x+2)=51x + (x+1) + (x+2) = 51\newline(x+x+x)+(1+2)=51(x + x + x) + (1+2) = 51\newline3x+3=513x + 3 = 51
  4. Isolate Variable Term: Isolate the variable term in 3x+3=513x + 3 = 51.
    3x+3=513x + 3 = 51
    3x+3−3=51−33x + 3 - 3 = 51 - 3
    3x=483x = 48
  5. Solve for x: 3x=483x = 48 \newlineSolve for x.\newline3x=483x = 48 \newline(3x)/3=48/3(3x)/3 = 48/3 \newlinex=16x = 16
  6. Final Consecutive Integers: We have: \newlinex=16x = 16 \newlineWhat are the 33 consecutive integers that add up to 5151?\newlineThree consecutive integers: \newlinex,x+1,x+2x, x+1, x+2 \newline16,16+1,16+216, 16+1, 16+2 \newline16,17,1816, 17, 18

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