Solving inequalities word problem

Question

One month Debra rented
2
movies and
5
video games for a total of
$33
. The next month she rented
8
movies and
3
video games for a total of
$30
. Find the rental cost for each movie and each video game.

Answer 1

Create a system of equations using the information given. I will represent movies with "m" and video games with "v"

 

2m + 5v = 33

8m + 3v = 30

 

Let's multiply the first equation by -4, so that way when we add the two equations together, the terms with "m" will cancel each other out.

 

(-4) x (2m + 5v = 33) = -8m - 20v = -132

 

-8m - 20v = -132

8m + 3v = 30

 

-17v = -102

v = 6

 

Now that we have a value for "v", plug that into either equation, and then solve for "m"

 

2m + 5v = 33

2m + 5(6) = 33

2m + 30 = 33

2m = 3

m = 1.5

 

The rental cost for each movie is $1.50

The rental cost for each video game is $6.00

Answer 2

Hi Mike!

 

The first step to answering inequality questions is to write out their equations! In this particular questions I will be using "m" to represent the rental cost of movies and "v" to represent the rental cost video games. The question tells us that these are the equations we are working with: 

 

2m + 5v = $33

8m + 3v = $30

 

From here, you will want to isolate a variable ("m" or "v") in one of the equations. This can easily be done by changing the first equation to:

 

2m = $33 - 5v

 

Now that we have isolated the variable 2m to equal $33 - 5v. We can replace 8m in the second equation to 4*(2m) since 2m times 4 is equal to 8m. So this is what you should get:

 

4*($33-5v) + 3v = $30

 

Now we have one equation with one variable! So solve for v:

 

a.) $132 - 20v + 3v = $30

b.) -20v + 3v = -$102

c.) -17v = -$102

d.) v = $6

 

Now that we solved for the rental cost for video games, we can easily find the rental cost for a movie by simply plugging in $6 to one of the equations! I will use the first equation:

 

a.) 2m + 5($6) = $33

b.) 2m + $30 = $33

c.) 2m = $3

d.) m = $1.50

 

So the rental cost of a movie is $1.50 and the rental cost of a video game is $6. You may checked this by plugging in the values into the second equation as well.

 

I hope you found this helpful!

 

- Jonathan