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There are 33 consecutive integers that have a sum of 3333. Which integers are they?\newline_\_, _\_, _\_

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Full solution

Q. There are 33 consecutive integers that have a sum of 3333. 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 that represents the sum of the three consecutive integers equal to 3333. Equation: x+(x+1)+(x+2)=33x + (x+1) + (x+2) = 33
  3. Simplify Equation: Simplify the equation by combining like terms.\newlinex+(x+1)+(x+2)=33x + (x+1) + (x+2) = 33\newline(x+x+x)+(1+2)=33(x + x + x) + (1+2) = 33\newline3x+3=333x + 3 = 33
  4. Isolate Variable Term: Isolate the variable term by subtracting 33 from both sides of the equation.\newline3x+3−3=33−33x + 3 - 3 = 33 - 3\newline3x=303x = 30
  5. Solve for x: Solve for x by dividing both sides of the equation by 33.\newline3x3=303\frac{3x}{3} = \frac{30}{3}\newlinex=10x = 10
  6. Find Consecutive Integers: Find the three consecutive integers using the value of xx.\newlineFirst integer: x=10x = 10\newlineSecond integer: x+1=10+1=11x + 1 = 10 + 1 = 11\newlineThird integer: x+2=10+2=12x + 2 = 10 + 2 = 12

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