City A has a current population of 156,289 residents and has an annual growth of 146 residents. City B has a current population of 151,293 and has an annual growth of 363 residents. Write an equation that represents when City A and City B will have the same

population.

A. 156,289 + 151,293р = 146 + 363р

B. 156,289 + 146р = 151,293 + 363р

С. 156,289р + 146 = 151,293р + 363

D. 156,289р + 151,293 = 146р + 363

To determine when City A and City B will have the same population, we need to set up an equation where the population of City A equals the population of City B.

Let \( r \) represent the number of years after the current year.

- **City A** has a current population of 156,289 and grows by 146 residents per year. So, the population of City A after \( r \) years is given by:  
  \[
  156,289 + 146r
  \]

- **City B** has a current population of 151,293 and grows by 363 residents per year. So, the population of City B after \( r \) years is given by:  
  \[
  151,293 + 363r
  \]

We want to find \( r \) such that the population of City A equals the population of City B:
\[
156,289 + 146r = 151,293 + 363r
\]

So, the correct answer is:

**B. \( 156,289 + 146r = 151,293 + 363r \)**

Would you like to go through the steps to solve this equation for \( r \)? 

Here are five related questions for further practice:
1. How would the equation change if City A's growth rate doubled?
2. What would be the population of each city after 10 years?
3. If the growth rates were switched, when would the populations be equal?
4. How long would it take for City B to surpass City A in population?
5. What if both cities had the same initial population but different growth rates?

**Tip:** When dealing with growth problems, always clearly define your variables and translate the problem into an equation step by step.

Learn how to solve the problem of determining when City A and City B will have the same population. Understand the concepts of population growth, linear equations, and how to set up and solve equations involving growth rates. Suitable for high school students and anyone interested in population dynamics.

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