plz solve this microeconomic problem. I don\'t know though I tried to solve this

Question

plz solve this microeconomic problem. I don't know though I tried to solve this problem all day..

The demand function for Coki-Cola is Q=a+bP+cP_m where O is quantity demanded of Coki-Cola, P is the price of Coki-Cola and P_m is the price of Mepsi-Cola. We found that the equilibrium quantity and price of Coki-Cola are 100 and $500, respectively and the equilibrium quantity and price of Mepsi-Cola are 200 and S400, respectively. Moreover, we also found that at the equilibrium, the own price elasticity (e_p) and the cross-price elasticity (_pm) of the demand of Coki-Cola are -2 and 1, respectively. Given the information, specify the demand function of Coca-Cola by calculating the values of a, b and c.

Explanation / Answer

Q= a+ bP +cPm

price elasticity of Coki cola= (dQ/dP )*Q/P

                                          = b*100/500   = -2    (given)

                                           b= - 10

cross elasticity of Coki cola= (dQ/dPm )*Q/Pm = c*100/400 = 1

                                                        c= 4

now after using equilibrium values of Q, P ,Pm , b and c, we will find out a

100= a+ (-10)(500 )+4(400)

100 =a - 3400

a= 3500

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