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There are 33 consecutive integers that sum to 4242. What are the integers?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_

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Full solution

Q. There are 33 consecutive integers that sum to 4242. 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 that represents the sum of the three consecutive integers equal to 4242.\newlineEquation: x+(x+1)+(x+2)=42x + (x+1) + (x+2) = 42
  3. Simplify Equation: Simplify the equation by combining like terms.\newlinex+(x+1)+(x+2)=42x + (x+1) + (x+2) = 42\newline(x+x+x)+(1+2)=42(x + x + x) + (1+2) = 42\newline3x+3=423x + 3 = 42
  4. Isolate Variable Term: Isolate the variable term by subtracting 33 from both sides of the equation.\newline3x+3−3=42−33x + 3 - 3 = 42 - 3\newline3x=393x = 39
  5. Solve for x: Solve for x by dividing both sides of the equation by 33.\newline3x3=393\frac{3x}{3} = \frac{39}{3}\newlinex=13x = 13
  6. Find Consecutive Integers: Find the three consecutive integers using the value of xx.\newlineFirst integer: x=13x = 13\newlineSecond integer: x+1=13+1=14x + 1 = 13 + 1 = 14\newlineThird integer: x+2=13+2=15x + 2 = 13 + 2 = 15

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