Suppose that the demand and supply for artificial Christmas trees is given by the functions below where $p$ is the price of a tree in dollars and $q$ is the quantity of trees that are demanded$/$supplied in hundreds. Find the price that gives the market equilibrium price and the number of trees that will be sold$/$bought at this price.

$p=106\mathrm{.}60-0\mathrm{.}10q(demand$ function$)$

$p=0\mathrm{.}01q^2+4\mathrm{.}84(supply$ function$)$

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A$.$ The equilibrium price of $ gives a demand that is equal to a supply of hundred trees. $($Simplify your answer. Type integers or simplified fractions.$)$

B$.$ The equilibrium price does not exist.