Let’s call the two numbers x and y. According to the problem, we have two equations:
- x + y = 18 (the sum)
- x – y = 6 (the difference)
We can solve these equations step by step. First, we can rearrange the second equation to express x in terms of y:
x = y + 6
Now, we can substitute this expression for x into the first equation:
(y + 6) + y = 18
This simplifies to:
2y + 6 = 18
Next, we subtract 6 from both sides:
2y = 12
Then, we divide both sides by 2:
y = 6
Now that we have y, we can find x using our earlier equation:
x = y + 6 = 6 + 6 = 12
Therefore, the two numbers we are looking for are 12 and 6. To confirm:
- Sum: 12 + 6 = 18
- Difference: 12 – 6 = 6
Both conditions are satisfied, so the solution is correct.