The number x of picture cellphones a manufacturer is willing to sell at price p is given by
x = p^2/5 − 20, where p is the price, in dollars, per picture cellphone. The number x of picture cellphones a distributor is willing to purchase is given by x = 51,948/p + 1, where p is the price, in dollars, per picture cellphone. Find the equilibrium price.

Question

The number x of picture cellphones a manufacturer is willing to sell at price p is given by 
x = p^2/5 − 20, where p is the price, in dollars, per picture cellphone. The number x of picture cellphones a distributor is willing to purchase is given by x = 51,948/p + 1, where p is the price, in dollars, per picture cellphone. Find the equilibrium price.

anonymous · Answer

are they asking you to solve 
$$x=\frac{51948}{p+1}\
x=p^{\frac{2}{5}}-20$$??

anonymous · Answer

yup

anonymous · Answer

$$\frac{51948}{p+1}=p^{\frac{2}{5}}-20$$
is a start 
then 
$$51948=(p+1)(p^{\frac{2}{5}}-20)$$
after that i guess we have to multiply out

anonymous · Answer

i don't think there is a nice algebra way to do this, i would use a computer http://www.wolframalpha.com/input/?i=51948%3D%28p%2B1%29%28p^ {\frac{2}{5}}-20%29

anonymous · Answer

this one should work http://www.wolframalpha.com/input/?i=51948%3D%28p%2B1%29%28p^%282%2F5%29-20%29

anonymous · Answer

wait. i wrote the wrong equation.. let me write it again

anonymous · Answer

$$x= \frac{ p^2 }{ 5 }-20$$
$$x= \frac{ 51948 }{p+1 }$$

anonymous · Answer

then this one is 
$$51948=(p+1)(\frac{1}{5}p^2-20)$$

anonymous · Answer

what's the next step sir?

anonymous · Answer

you will get a cubic equation if you multiply out 
you get 
$$p^3+p^2-100 p-259840 = 0$$ but it is not that easy to solve a cubic equation

anonymous · Answer

oh also i multiplied by 5 to get rid of the fraction in any case it turns out that one solution is $64$ but i only know that because of this http://www.wolframalpha.com/input/?i=%28x%2B1%29%28x^2-100%29%3D51948*5