To find three consecutive integers whose sum is 165, we can start by letting the first integer be represented as x. This means the next two consecutive integers will be x + 1 and x + 2.
We can set up the equation for their sum:
x + (x + 1) + (x + 2) = 165
Simplifying this, we combine like terms:
3x + 3 = 165
Next, we subtract 3 from both sides to isolate the term containing x:
3x = 165 – 3
3x = 162
Now, we divide both sides by 3:
x = 54
So, the first integer is 54. The other two consecutive integers are:
- Second integer: 54 + 1 = 55
- Third integer: 54 + 2 = 56
Thus, the three consecutive integers are 54, 55, and 56.