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A set of 33 consecutive integers adds up to 1515. Which integers are they?\newline_\_, _\_, _\_

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Full solution

Q. A set of 33 consecutive integers adds up to 1515. Which integers are they?\newline_\_, _\_, _\_
  1. Define First Integer: Let xx be the first integer.\newlineConsecutive integers increase by 11 each time.\newlineConsecutive integers: xx, x+1x+1, x+2x+2
  2. Set Up Equation: Set up the equation that represents the sum of 33 consecutive integers equal to 1515. Add three consecutive integers and equate the sum to 1515. Equation: x+(x+1)+(x+2)=15x + (x+1) + (x+2) = 15
  3. Simplify Equation: Simplify the left side of the equation x+(x+1)+(x+2)=15x + (x+1) + (x+2) = 15.x+(x+1)+(x+2)=15x + (x+1) + (x+2) = 15(x+x+x)+(1+2)=15(x + x + x) + (1+2) = 153x+3=153x + 3 = 15
  4. Isolate Variable Term: Isolate the variable term in the equation 3x+3=153x + 3 = 15.
    3x+3=153x + 3 = 15
    3x+3−3=15−33x + 3 - 3 = 15 - 3
    3x=123x = 12
  5. Solve for x: Solve for x.\newline3x=123x = 12\newline3x3=123\frac{3x}{3} = \frac{12}{3}\newlinex=4x = 4
  6. Determine Consecutive Integers: Determine the 33 consecutive integers that add up to 1515.\newlineThree consecutive integers:\newlinexx, x+1x+1, x+2x+2\newline44, 4+14+1, 4+24+2\newline44, 55, 151500

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