Question

find the point of equilibrium of the demand and supply equations. the point of equilibrium is the price p and the num supply equations.
demand
$p = 80 - 0.05x$
supply
$p = 15 + 0.2x$
$(x, p) = \left(\square\
ight)$

Explanation:

Step1: Set demand equal to supply

At equilibrium, demand price equals supply price, so set \( 80 - 0.05x = 15 + 0.2x \).

Step2: Solve for x

Add \( 0.05x \) to both sides: \( 80 = 15 + 0.25x \).
Subtract 15 from both sides: \( 65 = 0.25x \).
Divide by 0.25: \( x = \frac{65}{0.25} = 260 \).

Step3: Find p using x

Substitute \( x = 260 \) into demand equation: \( p = 80 - 0.05(260) = 80 - 13 = 67 \).

Answer:

\((260, 67)\)