sum of 3 consecutive odd integers equals 1 hundred 17 | MathCelebrity Forum

# sum of 3 consecutive odd integers equals 1 hundred 17

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sum of 3 consecutive odd integers equals 1 hundred 17

The sum of 3 consecutive odd numbers equals 117. What are the 3 odd numbers?

1) Set up an equation where our odd numbers are n, n + 2, n + 4
2) We increment by 2 for each number since we have odd numbers.
3) We set this sum of consecutive odd numbers equal to 117
n + (n + 2) + (n + 4) = 117

Simplify this equation by grouping variables and constants together:
(n + n + n) + 2 + 4 = 117
3n + 6 = 117

Subtract 6 from each side to isolate 3n:
3n + 6 - 6 = 117 - 6

Cancel the 6 on the left side and we get:
3n + 6 - 6 = 117 - 6
3n = 111

Divide each side of the equation by 3 to isolate n:
3n/3 = 111/3

Cancel the 3 on the left side:
3n/3 = 111/3
n = 37

Call this n1, so we find our other 2 numbers
n2 = n1 + 2
n2 = 37 + 2
n2 = 39

n3 = n2 + 2
n3 = 39 + 2
n3 = 41

List out the 3 consecutive odd numbers
(37, 39, 41)

37 ← 1st number, or the Smallest, Minimum, Least Value
39 ← 2nd number
41 ← 3rd or the Largest, Maximum, Highest Value