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Three consecutive integers sum to 2121. Which integers are they?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_

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Full solution

Q. Three consecutive integers sum to 2121. Which integers are they?\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 2121: x+(x+1)+(x+2)=21x + (x+1) + (x+2) = 21.
  3. Simplify Equation: Simplify the equation: x+x+1+x+2=21x + x + 1 + x + 2 = 21. Combine like terms: 3x+3=213x + 3 = 21.
  4. Isolate Variable Term: Isolate the variable term by subtracting 33 from both sides of the equation: 3x+3−3=21−33x + 3 - 3 = 21 - 3, which simplifies to 3x=183x = 18.
  5. Solve for x: Divide both sides of the equation by 33 to solve for x: 3x3=183\frac{3x}{3} = \frac{18}{3}, which simplifies to x=6x = 6.
  6. Find Consecutive Integers: Now that we have the value of xx, we can find the three consecutive integers: x=6x = 6, x+1=6+1x+1 = 6+1, x+2=6+2x+2 = 6+2. Therefore, the integers are 66, 77, and 88.

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