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The sum of three consecutive natural numbers is 11251125, find the numbers.\newlineThe three numbers in increasing order are xx, x+1x+1, and x+2x+2.

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Full solution

Q. The sum of three consecutive natural numbers is 11251125, find the numbers.\newlineThe three numbers in increasing order are xx, x+1x+1, and x+2x+2.
  1. Define First Natural Number: Let xx be the first natural number. Consecutive natural numbers increase by 11 each time. Consecutive natural numbers: xx, x+1x+1, x+2x+2
  2. Set Up Equation: Set up the equation that represents the sum of the three consecutive natural numbers equal to 11251125.\newlineEquation: x+(x+1)+(x+2)=1125x + (x+1) + (x+2) = 1125
  3. Simplify Equation: Simplify the left side of the equation x+(x+1)+(x+2)=1125x + (x+1) + (x+2) = 1125.x+(x+1)+(x+2)=1125x + (x+1) + (x+2) = 1125(x+x+x)+(1+2)=1125(x + x + x) + (1+2) = 11253x+3=11253x + 3 = 1125
  4. Isolate Variable Term: Isolate the variable term 3x3x in the equation 3x+3=11253x + 3 = 1125.
    3x+3=11253x + 3 = 1125
    3x+3−3=1125−33x + 3 - 3 = 1125 - 3
    3x=11223x = 1122
  5. Solve for x: Solve for x in the equation 3x=11223x = 1122.
    3x=11223x = 1122
    x=11223x = \frac{1122}{3}
    x=374x = 374
  6. Find Consecutive Numbers: Find the three consecutive natural numbers using the value of xx.\newlineFirst number: x=374x = 374\newlineSecond number: x+1=374+1=375x + 1 = 374 + 1 = 375\newlineThird number: x+2=374+2=376x + 2 = 374 + 2 = 376

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