Final answer:
The question asks for the equilibrium price and quantity for personal pizzas by solving the demand and supply equations algebraically, where the demand equation is QD = 400 - 20P, and the supply equation is QS = 100 + 10P.
Step-by-step explanation:
The question involves determining the equilibrium price and quantity in a market for personal pizzas using a system of equations that represents the demand and supply in the market. The demand equation is given by QD = 400 - 20P, where QD is the quantity demanded, and P is the price. The supply equation is QS = 100 + 10P, where QS is the quantity supplied. To find the equilibrium, we set quantity demanded equal to quantity supplied (QD = QS), and solve the resulting equation for P (price).
By equating the two equations, we get 400 - 20P = 100 + 10P. We can solve for P by combining like terms and dividing by the coefficient of P, which gives us the equilibrium price. Once we have the equilibrium price, we substitute it back into either the demand or supply equation to find the corresponding equilibrium quantity.