Question 145212
a) You are correct.


b) To find the fair price, replace the 2 with x and the -1.14 with 0 (since a "fair" price means that the player will break even) to get


{{{400(1/1000) + 200(1/1000) + 50(5/1000) -x(993/1000)=0}}}



{{{4/10 + 2/10 + 1/4 -x(993/1000)=0}}} Multiply



{{{17/20 -x(993/1000)=0}}} Combine like terms



{{{ -x(993/1000)=-17/20}}} Subtract {{{17/20}}} from both sides



{{{ -x*cross((993/1000))cross((-1000/993))=(-17/20)(-1000/993)}}} Multiply both sides by {{{-1000/993}}} to completely isolate x




{{{ x=850/993}}} Multiply



{{{ x=0.8559919}}} Use a calculator to approximate the fraction



{{{x=0.86}}} Round to the nearest hundredth



So the fair price of the ticket is about 86 cents.