The sum of three positive integers is 16. If the first integer is doubled, the sum is 22. If the third integer is tripled, the sum is 20. What are the 3 integers?

Solution:
Let x = First integer
y = Second integer
z = Third integer
x + y + z = 16 (Sum of the integers is 16)
2x + y + z = 22 (Double the first integer and the sum is 22)
x + y + 3z = 20 (Triple the third integer and the sum is 20)

We can eliminate both the y and z variable by subtracting the second equation from the first, therefore
x + y + z = 16
-(2x + y + z = 22)
-x = -6, x = 6

Subtract third equation from the first equation to eliminate the x and y variable, therefore
x + y + z = 16
-(x + y + 3z = 20)
-2z = -4, z = 2

Now substitute 6 for x and 2 for z in the first equation and solve for y.
6 + y + 2 = 16
8 + y = 16
y = 8

The three integers are 6, 8 and 2.