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The sum of 33 consecutive integers is 4242. Which integers are they?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_

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Full solution

Q. The sum of 33 consecutive integers is 4242. Which integers are they?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_
  1. Define First Integer: Let xx be the first integer.\newlineConsecutive integers increase by 11 each time.\newlineConsecutive integers: xx, x+1x+1, x+2x+2
  2. Set Up Equation: Set up the equation that represents the sum of 33 consecutive integers equal to 4242.\newlineEquation: x+(x+1)+(x+2)=42x + (x+1) + (x+2) = 42
  3. Simplify Equation: Simplify the left side of the equation x+(x+1)+(x+2)=42x + (x+1) + (x+2) = 42.x+(x+1)+(x+2)=42x + (x+1) + (x+2) = 42(x+x+x)+(1+2)=42(x + x + x) + (1+2) = 423x+3=423x + 3 = 42
  4. Isolate Variable Term: Isolate the variable term in 3x+3=423x + 3 = 42.\newline3x+3=423x + 3 = 42\newline3x+3−3=42−33x + 3 - 3 = 42 - 3\newline3x=393x = 39
  5. Solve for x: Solve for x.\newline3x=393x = 39\newline3x3=393\frac{3x}{3} = \frac{39}{3}\newlinex=13x = 13
  6. Determine Consecutive Integers: Determine the 33 consecutive integers that add up to 4242.\newlineThree consecutive integers:\newlinexx, x+1x+1, x+2x+2\newline1313, 13+113+1, 13+213+2\newline1313, 1414, 424200

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