SOLUTION: The supply and demand functions for chocolate ice cream are give by {{{S(p)= (1/6)p}}} and {{{ D (p)= 9 -(1/3)p}}}, where p represents the price in dollars. Find the equilibru

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: The supply and demand functions for chocolate ice cream are give by {{{S(p)= (1/6)p}}} and {{{ D (p)= 9 -(1/3)p}}}, where p represents the price in dollars. Find the equilibru      Log On


   



Question 316405: The supply and demand functions for chocolate ice cream are give by
S%28p%29=+%281%2F6%29p and +D+%28p%29=+9+-%281%2F3%29p,
where p represents the price in dollars.
Find the equilibruim price.

Answer by moshiz08(60) About Me  (Show Source):
You can put this solution on YOUR website!
Supply and demand are both functions of price. At the equilibrium price, supply equals demand. Thus, we are looking for a value of p such that S(p)=D(p). That is,
%281%2F6%29+p+=+9+-+%281%2F3%29+p+
and we must solve for p.
We can add %281%2F3%29p from both sides to get:
+%281%2F6%29p+%2B+%281%2F3%29p+=+9+
Combining the like terms on the left side gives
+%281%2F2%29+p+=+9
Thus, multiplying by 2 on both sides gives p+=+18.

Now we check: at p = 18, S(p)=%281%2F6%29+18+=+3 and D(p)=9-%281%2F3%2918=9-6=3, so the supply and demand are both equal to 3.