UpStudy Free Solution:

Let's denote the initial population of each part of the town as \(x\).

The population of the upper part of the town decreases by 20%, so the new population of the upper part is:

\[0.80x\]

The population of the lower part of the town increases by 15%, so the new population of the lower part is:

\[1.15x\]

The total population after these changes is given as 39,390. Thus, we can set up the equation:

\[0.80x + 1.15x = 39390\]

Combining the terms, we get:

\[1.95x = 39390\]

Solving for \(x\):

\[x = \frac { 39390} { 1.95} \]

\(\)

Therefore, the initial population of each part of the town was:

\[20200\]

Key Concepts:

1. Percentage Decrease and Increase: Percentage decrease or increase modifies the original value by a specific percentage. For example, a 10% decrease means the new value is 90% of the original, while a 25% increase means the new value is 125% of the original.

2. Linear Equation: A linear equation involves variables to the first power and represents a straight line when graphed. Solving it typically involves combining like terms and isolating the variable.

Explanation:

- Setting Up the Problem: Let's denote the initial amount as \(y\). If the amount decreases by 15%, the new amount becomes:

\(0.85y\)

Similarly, if the amount increases by 20%, the new amount becomes:

\(1.20y\)

- Formulating the Equation: Suppose the total new amount after these changes is known, say \(T\). The equation representing the combined changes would be:

\(0.85y + 1.20y = T\)

- Combining Terms: Combine like terms to simplify the equation:

\(2.05y = T\)

- Solving for \(y\): Solve the equation by isolating \(y\):

\(y = \frac { T} { 2.05} \)

With these concepts in mind, you can establish and solve linear equations concerning the percentage change. Get more personalized help and detailed, step-by-step solutions to your algebra equation problems with UpStudy AI Homework Solver! Receive detailed, adaptive support about UpStudy Sure, which equips you to understand any topic thoroughly while allowing you to define your best performance clearly. Try out UpStudy now; upgrade your learning process!