To solve the equations, we will substitute the expression for \( s \) into the equation, and then solve for \( p \).
We start with the two equations:
- \( 0.75s + 0.5p = 13 \)
- \( s = 20 - p \)
Substituting \( s \) from equation 2 into equation 1:
\[ 0.75(20 - p) + 0.5p = 13 \]
Now, distribute \( 0.75 \):
\[ 15 - 0.75p + 0.5p = 13 \]
Next, combine the terms involving \( p \):
\[ 15 - 0.75p + 0.5p = 15 - 0.25p \]
Thus, we rewrite the equation as:
\[ 15 - 0.25p = 13 \]
Now, isolate the \( p \) term by subtracting 15 from both sides:
\[ -0.25p = 13 - 15 \] \[ -0.25p = -2 \]
Now, divide by -0.25 to solve for \( p \):
\[ p = \frac{-2}{-0.25} = \frac{2}{0.25} = 2 \times 4 = 8 \]
Thus, the value of \( p \) is:
\[ \boxed{8} \]