Town A and Town B were located close to each other, and recently merged into one city. Town A had a population with $12 \%$ African Americans. Town B had a population with $8 \%$ African Americans. After the merge, the new city has a total of 4000 residents, with $9.2 \%$ African Americans. Write and solve a system of equations to find how many residents Town A and Town B used to have.
Town A used to have $\square$ residents, and Town B used to have $\square$ residents.
Answer
Final Answer: Town A used to have \(\boxed{1200}\) residents, and Town B used to have \(\boxed{2800}\) residents.
Step 1 ：Let's denote the number of residents in Town A as \(x\) and the number of residents in Town B as \(y\).
Step 2 ：We know that the total number of residents in the new city is 4000, so we have the equation \(x + y = 4000\).
Step 3 ：The percentage of African Americans in the new city is 9.2%, which means that the total number of African Americans is \(0.092 \times 4000 = 368\). The number of African Americans from Town A is \(0.12x\) and from Town B is \(0.08y\). So we have the equation \(0.12x + 0.08y = 368\).
Step 4 ：We can solve this system of equations to find the values of \(x\) and \(y\).
Step 5 ：The solution to the system of equations is \(x = 1200\) and \(y = 2800\).
Step 6 ：Final Answer: Town A used to have \(\boxed{1200}\) residents, and Town B used to have \(\boxed{2800}\) residents.
