For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1,000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price. 2x + 9p - 93 = 0 and 3x - 14p + 108 = 0
A) equilibrium quantity 6,000 units; equilibrium price $13
B) equilibrium quantity 12,000 units; equilibrium price $9
C) equilibrium quantity 6,000 units; equilibrium price $9
D) equilibrium quantity 12,000 units; equilibrium price $13

Question

Quizplus · Accepted Answer

To find the equilibrium quantity and price, we need to solve the system of equations 2x + 9p - 93 = 0 and 3x - 14p + 108 = 0. We can use any method to solve the system, but one convenient way is to solve for one variable in terms of the other in each equation and then equate the two expressions. Solving for x in terms of p in the first equation, we get x = (93 - 9p)/2. Substituting into the second equation, we get (93 - 9p)/2 * 3 - 14p + 108 = 0. Simplifying and solving for p, we get p = 9. Substituting into either equation to find x, we get x = 6,000. Therefore, the equilibrium quantity is 6,000 units and the equilibrium price is $9. Answer choice C matches this result.

For the Pair of Supply-And-Demand Equations, Where X Represents the Quantity