To solve the given system of equations and find the value of $\frac{x}{3}$, let's go step by step.

The given equations are: $x + y = 25 \quad \text{(Equation 1)}$ $x - y = 5 \quad \text{(Equation 2)}$

Step 1: Add the equations

Add Equation 1 and Equation 2 to eliminate $y$: $(x + y) + (x - y) = 25 + 5$ $2x = 30$

Step 2: Solve for $x$

Divide both sides by 2: $x = 15$

Step 3: Solve for $y$

Substitute $x = 15$ back into Equation 1: $15 + y = 25$ $y = 10$

Step 4: Calculate $\frac{x}{3}$

Now that we have $x = 15$, we can calculate $\frac{x}{3}$: $\frac{15}{3} = 5$

Final Answer

The value of $\frac{x}{3}$ is $\boxed{5}$.

Would you like any further details or explanations?

Here are some related questions to consider:

1. What is the value of $\frac{y}{2}$ given the same equations?
2. What is the sum of $x$ and $y$ in this problem?
3. If $x$ were doubled, what would the new value of $x + y$ be?
4. How would the solution change if the second equation were $x - y = 10$?
5. What is the geometric interpretation of the system of equations?

Tip: Always check your solution by substituting the values back into the original equations to ensure they satisfy both equations.