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There are 33 consecutive integers that sum to 5757. Which integers are they?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_

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Full solution

Q. There are 33 consecutive integers that sum to 5757. Which integers are they?\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 5757: x+(x+1)+(x+2)=57x + (x+1) + (x+2) = 57.
  3. Simplify Equation: Simplify the equation: x+x+1+x+2=57x + x + 1 + x + 2 = 57. Combine like terms: 3x+3=573x + 3 = 57.
  4. Isolate Variable Term: Isolate the variable term by subtracting 33 from both sides of the equation: 3x+3−3=57−33x + 3 - 3 = 57 - 3, which simplifies to 3x=543x = 54.
  5. Divide to Solve: Divide both sides of the equation by 33 to solve for xx: 3x3=543\frac{3x}{3} = \frac{54}{3}, which simplifies to x=18x = 18.
  6. Find Consecutive Integers: Now that we have the value of xx, we can find the three consecutive integers: x=18x = 18, x+1=18+1x+1 = 18+1, x+2=18+2x+2 = 18+2. Therefore, the integers are 1818, 1919, and 2020.

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