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There are 33 consecutive integers that add up to 3030. What are the integers?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_

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Full solution

Q. There are 33 consecutive integers that add up to 3030. What are the integers?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_
  1. Define Consecutive 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 3030.\newlineEquation: x+(x+1)+(x+2)=30x + (x+1) + (x+2) = 30
  3. Simplify Equation: Simplify the equation by combining like terms. \newlinex+(x+1)+(x+2)=30x + (x+1) + (x+2) = 30\newline(x+x+x)+(1+2)=30(x + x + x) + (1+2) = 30\newline3x+3=303x + 3 = 30
  4. Isolate Variable Term: Isolate the variable term by subtracting 33 from both sides of the equation.\newline3x+3−3=30−33x + 3 - 3 = 30 - 3\newline3x=273x = 27
  5. Solve for x: Solve for x by dividing both sides of the equation by 33.\newline3x3=273\frac{3x}{3} = \frac{27}{3}\newlinex=9x = 9
  6. Find Consecutive Integers: Find the three consecutive integers using the value of xx.\newlineFirst integer: x=9x = 9\newlineSecond integer: x+1=9+1=10x + 1 = 9 + 1 = 10\newlineThird integer: x+2=9+2=11x + 2 = 9 + 2 = 11

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