To solve the problem, we need to find three consecutive integers whose sum is 15. Let’s denote the first integer as x. Therefore, the three consecutive integers can be represented as:
- First integer: x
- Second integer: x + 1
- Third integer: x + 2
Now, we can set up the equation for their sum:
x + (x + 1) + (x + 2) = 15
Combining the terms, we get:
3x + 3 = 15
Next, we solve for x by subtracting 3 from both sides:
3x = 12
Now, divide both sides by 3:
x = 4
Now that we have the first integer, we can find the other two:
- First integer: 4
- Second integer: 4 + 1 = 5
- Third integer: 4 + 2 = 6
So, the three consecutive integers are 4, 5, and 6. To verify, we can check their sum:
4 + 5 + 6 = 15
This confirms that our solution is correct. The integers are indeed 4, 5, and 6.