Final answer:
To find the two numbers, we can set up a system of equations using the given information. Solving the system of equations gives us the values of the two numbers, which are 36 and 14.
Step-by-step explanation:
To find the two numbers, let's assign variables to them. Let's call one of the numbers x and the other number y.
We are given two pieces of information: the sum of the numbers is 50, and their difference is 22. We can write these equations:
We can solve this system of equations using the substitution method or the elimination method. For the sake of simplicity, let's use the elimination method:
Add the two equations together to eliminate the y variable: (x + y) + (x - y) = 50 + 22
This simplifies to: 2x = 72
Divide both sides of the equation by 2 to solve for x: x = 36
Substitute the value of x back into one of the original equations to solve for y: 36 + y = 50
Subtract 36 from both sides of the equation to isolate y: y = 14
Therefore, the two numbers are 36 and 14.