We are given the equation:

$\frac{2}{8} = \frac{5}{p + 10}$

Step 1: Simplify $\frac{2}{8}$

$\frac{2}{8} = \frac{1}{4}$

Now the equation becomes: $\frac{1}{4} = \frac{5}{p + 10}$

Step 2: Cross-multiply to eliminate the fractions

$1 \cdot (p + 10) = 4 \cdot 5$ $p + 10 = 20$

Step 3: Solve for $p$

Subtract 10 from both sides: $p = 20 - 10$ $p = 10$

Thus, the solution is: $p = 10$

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What happens if you change the numerator in the original equation to 3?
2. How would the solution change if you added 2 to both sides of the equation?
3. Can you solve a similar equation: $\frac{4}{6} = \frac{7}{x + 3}$?
4. How can you check if $p = 10$ is the correct solution?
5. How does cross-multiplication help in solving proportions?

Tip: Always simplify fractions as early as possible to make equations easier to solve.