One month Rachel rented 6 movies and 2 video games for a total of $36.

Question

One month Rachel rented 6 movies and 2 video games for a total of $36. The next month she rented 3 movies and 5 video games for a total of $39. Find the rental cost for each movie and each video game.

Rental cost for each movie:

Rental cost for each video game:

Answer 1

Set up a system to solve

m = number of movies

v = number of videos

6m + 2v = 36

3m + 5v = 39. Multiply by -2, then

6m + 2v = 36

-6m - 10v = -78, add the equations

m drops out

-8v = -42, Divide by -8

v = 5.25, now substitute

6m + 2(5.25) = 36

6m + 10.5 = 36

6m = 25.5 divide by 6

m = 4.25

movies cost $4.25

videos cost $5.25

Answer 2

Let x = price of movie and y = price of video game

So, for first month equation will be

6x + 2y = 36........(i)

And for other month equation will be

3x + 5y = 39.......(ii)

Use the elimination method by multiplying both sides of second equation by 2, so the second equation will become

2(3x + 5y = $39) = 6x + 10y = 78....... (iii)

Calculating (i) and (iii) equations

6x + 2y = 36

-(6x + 10y = 78)

-8y = -42 (as both sides of equal to has -ve sign, it will cancel out, so the equation will be

8y = 42

y = 42/8

y = 5.25

Now keeping value of y in equation (i)

6x + 2 x 5.25 = 36

6x + 10.50 = 36

6x = 36 - 10.50

6x = 25.50

x = 25.50/6

x = 4.25

Thus, price of movie = $4.25 and price of video game = $5.25

Answer check for 1st equation

6x + 2y = 36

6 x 4.25 + 2 x 5.25 = 36

25.50 + 10.50 = 36

36 = 36

Answer check for 2nd equation

3x + 5y = 39

3 x 4.25 + 5 x 5.25 = 39

12.75 + 26.25 = 39

39 = 39

Answer 3

One month Rachel rented 6 movies and 2 video games for a total of $36. The next month she rented 3 movies and 5 video games for a total of $39. Find the rental cost for each movie and each video game.

Set up a system of equations:

6m + 2v = 36

3m + 5v = 39

Use graphing method to solve

<iframe src="https://www.desmos.com/calculator/j485hqdwl0?embed" width="500px" height="500px" style="border: 1px solid #ccc" frameborder=0></iframe>

Movies cost $4.25 and Video games cost $5.25

Answer 4

This question produces what is called a System of Equations. These can be solved by either Substitution or Elimination. But first we must set it up.

We need to assign a variable for each unknown item, in this case it is Movies and Video games, so I will

Let M = cost of one Movie

Let V = cost of one Video game

One month Rachel rented 6 movies and 2 video games for a total of $36. becomes 6M + 2V = 36

The next month she rented 3 movies and 5 video games for a total of $39. becomes 3M + 5V = 39

To solve with Substitution, solve for one variable -- like V in the top equation, then plug it in for the V in the bottom equation.

6M + 2V = 36

-6M -6M

2V = 36 - 6M

Divide both sides (everything on both sides) by 2 and find V = 18 - 3M

Now put that into the bottom equation 3M + 5V = 39 Substituting becoves 3M + 5(18 - 3M) = 39

Now solve for M. Distribute the 5 into the parenthses

3M + 90 - 15M = 39

Combine like terms

-12M + 90 = 39

Subtract 90 from both sides

-12M = -51

divide both sides by -12 and find that M = 4.25 so the cost to rent 1 movie is $4.25

V = 18 - 3M (we found this by solving the top equation for V, so plug in 4.25 for M, and find V)

V = 18 - 3(4.25) = 5.25 so the cost to rent 1 video is $5.25

Then check to be sure these numbers work in both equations. (and they DO work)

By ELIMINATION is a much quicker solution: We want to eliminate one variable. Here is our original system of equations

6M + 2V = 36

3M + 5V = 39 If I would multiply this whole equation by (-2), there would be -6M on the bottom, then we would add vertically, and the top 6m + the bottom -6M would eliminate the variable M, and we would just solve the rest for V.

6M + 2V = 36 multiply everything in the bottom equation by -2

-6M + (-10V) = -78

Add vertically

0M - 8V = -42

divide by -8

V = 5.25, so again we found that a video costs $5.25 to rent.

Plug this into either the top or the bottom equation to find M

Top: 6M + 2V = 36 6M + 2(5.25) = 36

6M + 10.5 = 36

subtract 10.5 from both sides

6M = 25.5

divide both sides by 6

M = 4.25 - again we find that the cost to rent one movie is $4.25

Answer 5

Let x = cost to rent a movie and let y = cost to rent a video game.

Then, 6x + 2y = 36 and 3x + 5y = 39.

From the first equation, y = -3x + 18.

Substituting for y in the other equation, we have 3x + 5(-3x + 18) = 39

So, -12x + 90 = 39

-12x = -51

x = $4.25 and y = -3(4.25) + 18 = $5.25