have a problem with this math question

Question

One month Boris rented 5  movies and 6  video games for a total of $42 . The next month he rented 3  movies and 2  video games for a total of $16 . Find the rental cost for each movie and each video game.

Answer 1

Hi Carol!

Let m = cost for a movie

Let v = cost of a video game

You'll have a system of 2 equations

cost of movies + cost of video games = total cost

5m + 6v = 42

3m + 2v = 16

The easiest variable to eliminate here will be v.

If you multiply the second equation by -3, you

will be able to cancel the variable v when added

to the first equation.

-3(3m + 2v = 16)

-9m -6v = -48 multiply -3 through parentheses

5m + 6v = 42

+ -9m - 6v = -48 add the first equation to the modified 2nd equation

-----------------

-4m = -6

----- ---- divide both sides -4

-4 -4

m = 1.50 (the cost of a movie is $1.50)

Now, plug this into one of the previous equations.

I'll plug into the original second equation.

3m + 2v = 16

3(1.50) + 2v = 16

4.50 + 2v = 16

-4.50 -4.50 subtract 4.50 from both sides

--------------------

2v = 11.50

--- ------- divide both sides by 2

2 2

v = 5.75 (cost of a video game is $5.75)

So, rental of a movie is $1.50 and the video game rents for $5.75

Answer 2

You need to set up an equation for each month. X will be movies and Y will be video games.

5X + 6Y = 42

and

3X + 2Y = 16

You could solve for X (or Y for that matter) for either of the equations but it'll be quicker and easier in the long run if you multiply everything in the second equation by 3.

9X +6Y = 48 solving for 6Y, the equation is then: 6Y = 48 - 9X

Plug this result in for 6Y on the first equation, and then solve for X

5X + (48-9X) = 42

-4X = -6

X = 1.5 So, each movie (X) costs $1.50. Then plug this back into either equation to find Y.

3(1.5) + 2Y = 16

2Y = 11.5

Y = 5.75 So, each video (Y) costs $5.75.