The sum of two numbers is 22 and their difference is 6. Find the numbers.

To solve this problem, we can set up a system of equations based on the information given.

Let’s denote the two numbers as x and y.

• The first equation based on their sum is: x + y = 22
• The second equation based on their difference is: x – y = 6

Now, we can solve the system of equations. We can start by adding the two equations to eliminate y:

x + y = 22
x - y = 6
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2x = 28

Now, divide both sides by 2:

x = 14

Now that we have found x, we can substitute it back into one of the original equations to find y. We’ll use the first equation:

14 + y = 22

Subtract 14 from both sides:

y = 8

Therefore, the two numbers are 14 and 8. To verify, we can check both the sum and the difference:

• Sum: 14 + 8 = 22
• Difference: 14 – 8 = 6

Both conditions are satisfied, confirming that the two numbers are indeed 14 and 8.