Linear population change: City A has population 136000 decreasing by 2400 per year, and City B has population 84000 increasing by 1600 per year. After how many years will their populations be equal?

Introduction / Context:
This problem models two populations changing linearly but in opposite directions. We set both expressions equal and solve for time. It is a straightforward linear equation in t (years).

Given Data / Assumptions:

• City A at t years: A(t) = 136000 - 2400*t
• City B at t years: B(t) = 84000 + 1600*t
• Equality A(t) = B(t)

Concept / Approach:
Equate A(t) and B(t) to find the year where the populations match. Since both changes are linear with constant rates, a single solution exists if rates differ.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 15, 18, 19: Substitution yields mismatched populations, so they are incorrect.

Common Pitfalls:

• Sign errors when moving terms (mixing +1600t and -2400t).
• Arithmetic errors dividing 52000 by 4000.

Final Answer: