Hi there, THE PROBLEM: The demand function for a particular product is given by p + 10q = 460 while supply for the product is given by p - 10q = -240 a) Find the market equilibrium quantity and price b) If the price per product is set at $50, will there be a shortage or a surplus in the market? SOLUTION: Part (a) Equilibrium quantity and price are found at the point the equations for supply and demand intersect. To find these values, solve the two equations as a system. In this case, you can solve by the substitution method. Step 1. Solve both equations for p. p + 10q = 460 p = -10q + 460 p - 10q = -240 p = 10q - 240 Step 2. Since p equals -10q+460 AND p equals 10q-240, those quantities must also be equal to each other. (This is called the Transitive Property.) Set them equal to each other and solve for q. -10q + 460 = 10q -240 Subtract 10q from both sides. -10q -10q + 460 = -10q + 10q -240 Combine like terms and simplify. -20q + 460 = -240 Subtract 460 from both sides. -20q +460 - 460 = -240 - 460 Combine like terms and simplify. -20q = -700 Divide both sides by -20. -20q/-20 = -700/-20 Simplify. q = 35 In the context of this problem, q = 35 means that the equilibrium quantity is 35 units of the product. Step 3. Now substitute 35 for q in either one of the original equations. (I'll use the first.) p + 10q = 460 p + 10(35) = 460 Simplify. p + 350 = 460 Subtract 350 from both sides. p + 350 - 350 = 460 - 350 Combine like terms and simplify. p = 110 In the context of this problem, p = 110 means that the equilibrium price is $110 for each unit of the product. Part (b) In this case we want to know how a price of $50 will effect supply and demand. If supply is greater than demand, there is a surplus. If supply is less than demand, there is a shortage. Step 1. Substitute $50 for p in the Supply and demand equations. DEMAND: p + 10q = 460 (50) + 10q = 460 Subtract 50 from both sides. 10q = 460 - 50 10q = 410 Divide both sides by 10. q = 41 When the the price is set at $50, the market demand is 41 units of product. SUPPLY: p - 10q = -240 (50) - 10q = -240 Subtract 50 from both sides. -10q = -240 - 50 -10q = -290 Divide both sides by -10. q = 29 When the price is set at $50, the market supply is 29 units of product. Since the supply of product (29) is less than the demand for product (41), there is a shortage. Hope this helps. Feel free to email if you have questions about the solution. Mrs. Figgy math.in.the.vortex@gmail.com