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A set of 33 consecutive integers adds up to 4848. Which integers are they?\newline_\_, _\_, _\_

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Full solution

Q. A set of 33 consecutive integers adds up to 4848. 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 4848.\newlineEquation: x+(x+1)+(x+2)=48x + (x+1) + (x+2) = 48
  3. Simplify Equation: Simplify the left side of the equation x+(x+1)+(x+2)=48x + (x+1) + (x+2) = 48.\newlinex+(x+1)+(x+2)=48x + (x+1) + (x+2) = 48\newline(x+x+x)+(1+2)=48(x + x + x) + (1+2) = 48\newline3x+3=483x + 3 = 48
  4. Isolate Variable Term: Isolate the variable term in 3x+3=483x + 3 = 48.
    3x+3=483x + 3 = 48
    3x+3−3=48−33x + 3 - 3 = 48 - 3
    3x=453x = 45
  5. Solve for x: Solve for x.\newline3x=453x = 45\newline3x3=453\frac{3x}{3} = \frac{45}{3}\newlinex=15x = 15
  6. Determine Consecutive Integers: Determine the 33 consecutive integers that add up to 4848.\newlineThree consecutive integers:\newlinexx, x+1x+1, x+2x+2\newline1515, 15+115+1, 15+215+2\newline1515, 1616, 484800

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