Question 1154041

let movies be {{{m}}} and video games {{{v}}}

if one month Alonzo rented {{{2}}} movies and {{{3}}} video games for a total of ${{{24}}}, we have

{{{2m+3v=24}}} ......solve for {{{m}}}

{{{2m=24-3v}}}

{{{m=12-3v/2}}}........eq.1



if the next month he rented {{{4}}} movies and {{{8}}} video games for a total of ${{{61}}}, we have

{{{4m+8v=61}}} ......solve for {{{m}}}

{{{4m=61-8v}}}

{{{m=61/4-2v}}}........eq.2


from eq.1 and eq.2 we have


{{{12-3v/2=61/4-2v}}}.....solve for {{{v}}}

{{{12-61/4=3v/2-2v}}}

{{{48/4-61/4=3v/2-4v/2}}}

{{{-13/4=-v/2}}}.....switch sides

{{{v/2=13/4}}}

{{{v=2(13/4)}}}

{{{v=(13/2)}}}

{{{v=6.50}}}


go to

{{{m=12-3v/2}}}........eq.1, substitute {{{v}}}

{{{m=12-(3*6.50)/2}}}

{{{m=12-9.75}}}

{{{m=2.25}}}


=> the rental cost for each movie is ${{{2.25}}} and each video game is ${{{6.50}}}