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

Question 316405: The supply and demand functions for chocolate ice cream are give by
and ,
where p represents the price in dollars.
Find the equilibruim price.
Answer by moshiz08(60) (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,

and we must solve for p.
We can add from both sides to get:

Combining the like terms on the left side gives

Thus, multiplying by 2 on both sides gives .

Now we check: at p = 18, S(p)= and D(p)=, so the supply and demand are both equal to 3.
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