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There are 33 consecutive integers with a sum of 5454. What are the integers?\newline_\_, _\_, _\_

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Full solution

Q. There are 33 consecutive integers with a sum of 5454. 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 5454.\newlineEquation: x+(x+1)+(x+2)=54x + (x+1) + (x+2) = 54
  3. Simplify Equation: Simplify the equation by combining like terms.\newlinex+x+x+1+2=54x + x + x + 1 + 2 = 54\newline3x+3=543x + 3 = 54
  4. Isolate Variable Term: Isolate the variable term by subtracting 33 from both sides of the equation.\newline3x+3−3=54−33x + 3 - 3 = 54 - 3\newline3x=513x = 51
  5. Solve for x: Solve for x by dividing both sides of the equation by 33.\newline3x3=513\frac{3x}{3} = \frac{51}{3}\newlinex=17x = 17
  6. Find Consecutive Integers: Find the three consecutive integers using the value of xx.\newlineFirst integer: x=17x = 17\newlineSecond integer: x+1=17+1=18x + 1 = 17 + 1 = 18\newlineThird integer: x+2=17+2=19x + 2 = 17 + 2 = 19

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