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The sum of three consecutive odd integers is 117 . Form an equation and solve it to find the integers.

The sum of three consecutive odd integers is 117117 . Form an equation and solve it to find the integers.

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Full solution

Q. The sum of three consecutive odd integers is 117117 . Form an equation and solve it to find the integers.
  1. Define Odd Integers: Let's call the first odd integer xx. Since we're dealing with odd integers, the next ones will be x+2x+2 and x+4x+4.
  2. Write Equation: Now, let's write the equation: x+(x+2)+(x+4)=117x + (x+2) + (x+4) = 117.
  3. Simplify Equation: Simplify the equation: 3x+6=1173x + 6 = 117.
  4. Subtract and Simplify: Subtract 66 from both sides: 3x+6−6=117−63x + 6 - 6 = 117 - 6, which simplifies to 3x=1113x = 111.
  5. Find Value of x: Divide both sides by 33 to find x: 3x3=1113\frac{3x}{3} = \frac{111}{3}, so x=37x = 37.
  6. Find Other Integers: Now we find the other two integers: x+2=37+2=39x+2 = 37+2 = 39 and x+4=37+4=41x+4 = 37+4 = 41.
  7. Check Sum: Let's check if they add up to 117117: 37+39+41=11737 + 39 + 41 = 117.

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