Let's solve the equation step by step.
You have two equations:
- \( 3c + 2.5p = 31 \)
- \( c = 11 - p \)
Now, we'll substitute equation 2 into equation 1:
\[ 3(11 - p) + 2.5p = 31 \]
Now, distribute the 3:
\[ 33 - 3p + 2.5p = 31 \]
Combine like terms \(-3p + 2.5p\):
\[ 33 - 0.5p = 31 \]
Next, subtract 33 from both sides:
\[ -0.5p = 31 - 33 \] \[ -0.5p = -2 \]
Now, divide both sides by -0.5:
\[ p = \frac{-2}{-0.5} = 4 \]
Thus, the value of \( p \) is:
\[ \boxed{4} \]