Answer:
The smallest of the seven integers is 432
Need-to-know:
First off, what are consecutive integers?
-> Consecutive integers are whole numbers that go one after the other without gaps
-> Examples include 1, 2, 3 ,4, ... or 123, 124, 125, ...
Explanation:
This problem has seven consecutive integers adding up to a single total. If the first, smallest of the seven, is equal to x, then the second will be x + 1. Using this pattern, the third will be x + 2, fourth will be x + 3, etc.
Let's turn this into a mathematical equation;
(x) + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) = 3,045
Now we will "distribute" the positive, nothing will really change;
x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 3,045
Next we can "reorder" the terms. Since we are only using addition we can do this;
x + x + x + x + x + x + x + 1 + 2 + 3 + 4 + 5 + 6 = 3,045
Finally, we can combine like terms;
7x + 21 = 3,045
Now we will subtract 21 from both sides of the equation;
7x = 3,024
Last, we can divide both sides of the equation by 7 to find our answer;
x = 432
Checking our work:
432 + 433 + 434 + 435 + 436 + 437 + 438 = 3,045 ✓
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather