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The sum of 33 consecutive integers is 3636. What are the integers?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_

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Full solution

Q. The sum of 33 consecutive integers is 3636. 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 3636.\newlineEquation: x+(x+1)+(x+2)=36x + (x+1) + (x+2) = 36
  3. Simplify Equation: Simplify the equation by combining like terms.\newlinex+(x+1)+(x+2)=36x + (x+1) + (x+2) = 36\newline(x+x+x)+(1+2)=36(x + x + x) + (1+2) = 36\newline3x+3=363x + 3 = 36
  4. Isolate Variable Term: Isolate the variable term by subtracting 33 from both sides of the equation.\newline3x+3−3=36−33x + 3 - 3 = 36 - 3\newline3x=333x = 33
  5. Solve for x: Divide both sides of the equation by 33 to solve for x.\newline3x3=333\frac{3x}{3} = \frac{33}{3}\newlinex=11x = 11
  6. Find Consecutive Integers: Determine the three consecutive integers using the value of xx.\newlineFirst integer: x=11x = 11\newlineSecond integer: x+1=11+1=12x + 1 = 11 + 1 = 12\newlineThird integer: x+2=11+2=13x + 2 = 11 + 2 = 13

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