Question

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?

Answer 1

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