Let’s denote the two numbers as x and y.
According to the problem, we have the following relationships:
- x = 3y + 2 (one number is 2 more than 3 times another)
- x + y = 22 (their sum is 22)
Now, we can substitute the expression for x from the first equation into the second equation:
(3y + 2) + y = 22
This simplifies to:
- 3y + 2 + y = 22
- 4y + 2 = 22
- 4y = 20
- y = 5
Now that we have the value of y, we can find x:
x = 3(5) + 2 = 15 + 2 = 17
Therefore, the two numbers are:
- x = 17
- y = 5
In conclusion, the two numbers are 17 and 5.