We have a system of two equations:

1. \( x + y = 96 \)
2. \( 0.25x + 0.10y = 15.00 \)

To solve this system of equations, we can use substitution or elimination. Let's use substitution for this case.

### Step 1: Solve the first equation for \( y \)
From the first equation \( x + y = 96 \), solve for \( y \):

\[
y = 96 - x
\]

### Step 2: Substitute \( y = 96 - x \) into the second equation
Substitute \( y \) in the second equation:

\[
0.25x + 0.10(96 - x) = 15.00
\]

Distribute the 0.10:

\[
0.25x + 9.6 - 0.10x = 15.00
\]

### Step 3: Combine like terms
Combine the \( x \)-terms on the left side:

\[
0.15x + 9.6 = 15.00
\]

### Step 4: Solve for \( x \)
Subtract 9.6 from both sides:

\[
0.15x = 5.4
\]

Now, divide by 0.15:

\[
x = \frac{5.4}{0.15} = 36
\]

### Step 5: Substitute \( x = 36 \) back into the equation for \( y \)
Now substitute \( x = 36 \) into \( y = 96 - x \):

\[
y = 96 - 36 = 60
\]

### Final Solution:
The solution to the system of equations is:
\[
x = 36, \quad y = 60
\]

Would you like more details on any of these steps or have any questions?

### Related Questions:
1. How can the elimination method be used to solve this system of equations?
2. What are some real-world applications of solving such systems of equations?
3. Can we graphically represent the solution of the system?
4. How would the solution change if the coefficients in the second equation were different?
5. What methods are available to check if the solution is correct?

### Tip:
Always check your solution by substituting the values back into the original equations to ensure accuracy.

Learn how to solve the system of equations x + y = 96 and 0.25x + 0.10y = 15.00 using the substitution method with a step-by-step solution. This problem covers systems of linear equations and is suitable for high school students.

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