Question

Three consecutive integers have a sum of 135 . find the integers.

Answer 1

Let the smallest number be x.
The other 2 numbers are x + 1 and x + 2.

Their sum is 135.
⇒ x + ( x + 1) + (x + 2) = 135

Solve for x:
x + ( x + 1) + (x + 2) = 135

Remove brackets:
x + x + 1 + x + 2 = 135

Combine like terms:
3x + 3 = 135

Subtract 3 from both sides:
3x = 132

Divide both sides by 3:
x = 44

Find the numbers:
Smallest number = x = 44
Middle number = x + 1 = 44 + 1 = 45
Last number = x + 2 = 44 + 2 = 46

Answer: The numbers are 44, 45 and 46

Answer 2

Three consecutive integers can be represented as followed.

X → first integer

X + 1 → second integer

X + 2 → third integer

Since the sum of our three consecutive integers is 135, we can set up an equation to represent this.

X + X + 1 + X + 2 = 135

-Simplify on the left-

3x + 3 = 135

-3 -3

3x = 132

÷3 ÷3 ← divide both sides by 3

X = 44

X + 1 = 45

X + 2 = 46

Therefore, the three consecutive integers are 44, 45, and 46.