To find the two numbers, we can set up a system of equations based on the information given.
Let the two numbers be x and y.
We have the following equations:
- x + y = 21 (Equation 1: the sum of the numbers)
- x – y = 5 (Equation 2: the difference of the numbers)
Now, we can solve these equations. We can start by adding Equation 1 and Equation 2:
Suppose we add:
- (x + y) + (x – y) = 21 + 5
This simplifies to:
- 2x = 26
From here, we can solve for x:
- x = 26 / 2 = 13
Now that we have x = 13, we can substitute this value back into Equation 1 to find y:
13 + y = 21 leads to:
- y = 21 – 13 = 8
So, the two numbers are 13 and 8.
To verify, we can check the conditions:
- The sum is: 13 + 8 = 21
- The difference is: 13 – 8 = 5
Both conditions are satisfied, confirming our solution.