To find two numbers that satisfy both conditions—a sum of 17 and a difference of 5—we can set up a couple of equations.
Let’s call the two numbers x and y. According to the problem, we can create the following equations:
- x + y = 17 (the sum)
- x – y = 5 (the difference)
Next, we can solve these equations step by step. First, we can add both equations together:
(x + y) + (x – y) = 17 + 5
This simplifies to:
2x = 22
From this, we find:
x = 11
Now that we have x, we can use the first equation to find y:
11 + y = 17
This leads us to:
y = 6
So the two numbers we are looking for are 11 and 6.
To confirm our solution, we can check both conditions:
- The sum: 11 + 6 = 17
- The difference: 11 – 6 = 5
Both conditions are satisfied! Therefore, the two numbers are 11 and 6.