one month lamar rented 3 movies and 5 video games for a total of $40. the next month he rented 12 movies and 2 video games for a total of $43. find the rental cost for each movie and each video game.
rental cost for each movie: $
rental cost for each video game: $__

movies are $2.50 and video games are $6.50

Step-by-step explanation:

We have a system of equations that results from this information.  The first equation is

3m + 5v = 40, which says that 3 movies at the cost of "m" each plus 5 video games at the cost of "v" each add up to equal $40.

The second equation is

12m + 2v = 43, which says that 12 movies at the cost of "m" each plus 2 video games at the cost of "v" each add up to equal $43.

We can solve them by the addition/elimination method:

  3m   +   5v   =   40

 12m   +   2v   =   43

Let's multiply the first equation by a -4 to eliminate the m's first.  Doing that muliplication gives you the new equation in the system as

   -12m   -   20v    =    -160

    12m   +     2v    =       43

You can see that m's are eliminated, and doing the addition of what remains gives you the simpler equation:

-18v = -117 and

v = $6.50

Now we can use that value of v to solve for m:

3m + 5(6.50) = 40 so

3m + 32.5 = 40 and

3m = 7.5 so

m = $2.50

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