Algebra question please answer

Question

Supposed that the demand D for candy at a theater is inversely related to the price p. When the price of candy is $3.00 per bag, the theater sells 221 bags of candy. Determine the number of bags of candy that will be sold if the price is raised to $3.25 a bag.

Answer 1

P=k/x

3 = k/221

k = 663

P = 663/x

3.25 = 663/x

x = 663/3,25 = 204 bags sold

it comes out even and that's probably the answer you want

"inversely related" could also mean

P = -kx + b, a linear relationship, where b = the price where people stop buying anything. but you don't have enough information to solve it

3 =-k(221) + b, one equation 2 unknowns has an infinite number of solutions.

If you use the the solution of 204 at 3.25 and make it into a linear demand curve

3.25= -k(204) + b, subtract the 2 equations to get

.25 = 17k

k =1/68

P=-x/68 + 6.25 where if you charge $6.25 no one buys any candy

with the first inverse relation, it's a hyperbolic curve where there is no maximum price. keep charging more and someone out there is still buying.

with P=-663/x the revenue = Px = $663.00 at any price, which is not very realistic. the demand curve is unit elastic everywhere.

with P=-x/68 +6.25 revenue = Px = -x^2/68 + 6.25x

take the derivative and set it = 0 to find the revenue maximizing bags sold

-2x/68 + 6.25 = 0

x = 6.25(34) = 212.5

P= -212.5/68 + 6.26 = about $3.13 to maximize revenue, which is halfway between $3 and $3.25

maximum revenue = Px = 3.125(212.5) = about $664.06 = virtually the same as the max revenue with the hyperbolic equation.

"inversely related" means as P goes up, x goes down. That's consistent with either a hyperbolic or linear relation. Since you really don't have enough information to solve for a linear relation, go with the the P=663/x equation.