Duncan picks a number and will subtract 6 each second. george picks a different number and will add 8 each second. they begin at the same time, and after 14 seconds, they both arrive at the number 25 . what is the sum of duncan’s and george’s starting numbers?

To answer, let's set up a system of equations:
For Duncan: 
-6(14) + b = 25, where b is his starting number 

For George: 
8(14) + c = 25, where c is his starting number

Solving for b:
-6(14) + b = 25
-84 + b = 25           Add 84 to both sides
b = 109
Solving for c
8(14) + c = 25
112 + c = 25          Subtract 112 from both sides
c = -87

Duncan's number was 109, and George's number was -87
Their sum is: 
109 +  (-87) = 22
Answer is 22