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There are 33 consecutive integers that sum to 3939. What are the integers?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_

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Full solution

Q. There are 33 consecutive integers that sum to 3939. 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 3939: x+(x+1)+(x+2)=39x + (x+1) + (x+2) = 39.
  3. Simplify Equation: Simplify the equation: x+x+1+x+2=39x + x + 1 + x + 2 = 39. Combine like terms: 3x+3=393x + 3 = 39.
  4. Isolate Variable Term: Isolate the variable term by subtracting 33 from both sides of the equation: 3x+3−3=39−33x + 3 - 3 = 39 - 3, which simplifies to 3x=363x = 36.
  5. Divide to Solve: Divide both sides of the equation by 33 to solve for xx: 3x3=363\frac{3x}{3} = \frac{36}{3}, which simplifies to x=12x = 12.
  6. Find Consecutive Integers: Now that we have the value of xx, we can find the three consecutive integers: x=12x = 12, x+1=12+1x+1 = 12+1, x+2=12+2x+2 = 12+2. Therefore, the integers are 1212, 1313, and 1414.

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