Word problem

Question

At the local video rental store, jose rents 2 movies and 3 games for a total of $15.50. At the same time  Meg rents 3 movies and 1 game for a total of $12.05. How much money is needed to rent a combination of one game and one movie? 

Answer 1

Hi Fanny!

When working with word problems, the best thing to do is start off by turning the words into math equations. 

Jose rents 2 movies and 3 games for a total of $15.50. 

2m + 3g = 15.5

 

Meg rents 3 movies and 1 game for a total of $12.05.

3m + g = 12.05

 

Now that we have two equations, we will need to use them both to figure out the value of the variables (m and g). To do that, we are going to need to plug in one equation into the other. Right now, we can't really do that. First, we need to rearrange one of the equations. The easiest way to do that will to be to take Meg's equation and rearrange it to describe the value of one game. 

 

Original Meg equation: 3m + g = 12.05

Subtract 3m from each side: g = 12.05 - 3m

 

Now we have the Meg equation in a form where we can plug it in to the Jose equation, because now it describes the value of a video game rental as $12.05 minus the cost of three movies. 

 

Original Jose equation: 2m + 3g = 15.5

Insert value of g (from Meg equation: 2m + 3(12.05 - 3m) = 15.5

Distribute: 2m + 3(12.05) - 3(3m) = 15.5

Multiply: 2m + 36.15 - 9m = 15.5

Rearrange to put like terms together: 2m - 9m = 15.5 - 36.15

Combine like terms: -7m = -20.65

Multiply both sides by -1: -1 * -7m = -1 * -20.65

Multiply: 7m=20.65

Divide both sides by 7 to get value of m: m = 2.95

 

Now we know the value of a movie! It's $2.95! We can plug this in to the original Meg equation to find the value of the game. 

 

Original Meg equation: 3m + g = 12.05

Insert value of m: 3(2.95) + g = 12.05

Multiply: 8.85 + g = 12.05

Subtract to isolate g: g = 12.05 - 8.85

Subtract: g = 3.2

 

Now we have the value of g (3.2) and m (2.95), so it's super-simple to find out the cost of renting one game and one movie - just add them together!

 

Cost of renting one game and one movie: g + m

Substitute values of g and m: 3.2 + 2.95

Add: 6.15

 

There's our answer! Renting one game and one movie costs $6.15!

I hope this was helpful, Fanny!

Amanda

Answer 2

m- cost of renting movie

 

g - cost of renting a video

 

  2m + 3g = 15.50

 -3(3m  + g  = 12.05)

- 7m = 15.50 - 36.15

 

   - 7m = -20.65

 

    m =$2.95 

 

     3g = 15.50 - 5.90= 9.60

 

      g= $3.20

 

      $ 2.95 + $3.20 = $6.15

 

 

     

        

Answer 3

Create equations for Jose and Meg, using different variables for movies and games. I'll use then m for movies and g for games.

 

Jose: 15.50 = 2m + 3g

Meg: 12.05 = 3m + g

 

Since the second equation already has one variable isolated (there is only one g), we'll work with that one. Rearrange that equation to isolate g on one side of the equals sign by subtracting 3m from both sides.

 

g = - 3m + 12.05

 

Now plug in the g= equation where you see g in the first equation.

 

15.50 = 2m + 3(-3m + 12.05)

 

Now there is only one variable to solve for at this point: m.

 

15.50 = 2m - 9m + 36.15 = -7m + 36.15

 

Subtract 36.15 from both sides. Simplify and switch all to positive (since you can't have a negative number of movies or amount of money).

 

-20.65 = -7m --> 7m = 20.65

 

Divide by 7 to isolate the m: m = 2.95

 

Now that you know the value of m, plug it into either original equation to solve for g. I'll use the second one.

 

12.05 = 3(2.95) + g

12.05 = 8.85 + g

 

Subtract 8.85 from both sides to get g: g = 3.20

 

So a movie costs $2.95 and a game costs $3.20. The questions asked how much you would need to rent one of each, so add the two together.

 

Let T= total cost

T = m + g

T = 2.95 + 3.20 = 6.15

 

So you're answer is $6.15

Answer 4

2m+3g=$15.50

3m+g=$12.05

g=12.05-3m

substitute

2m+3(12.05-3m)=15.5

2m+36.15-9m=15.5

-7m+36.15=15.5

-7m=15.5-36.15

-7m=-20.65

m=20.65/7

m=$2.95 for one movie

3(2.95)+g=12.05

8.85+g=12.05

g=12.05-8.85

g=$3.20 for one game

$2.95+$3.20=$6.15 for one of each

Answer 5

Let x = the unknown cost of renting a movie

Let y = the unknown cost of renting a game

 

We have two unknowns (x and y), so we need two equations to solve for the two unknowns.

 

Equation 1 is "jose rents 2 movies and 3 games for a total of $15.50" which is written as:

 

2x + 3y = 15.50

 

Equation 2 is "Meg rents 3 movies and 1 game for a total of $12.05"

 

3x + y = 12.05

 

Solving for y in equation 2:

 

y = 12.05 - 3x

 

Now substitute 12.05 - 3x in place of the y in equation 1:

 

2x + 3(12.05 - 3x) = 15.50

2x+ 36.15 - 9x = 15.50

-7x = -20.65

 x = (-20.65)/(-7) = $2.95 

 

It costs $2.95 to rent a movie.  The value of y (cost to rent a game) can be determined from y = 12.05 - 3x  (x = 2.95).  Complete the calculation yourself.

 

The cost to rent one game and one movie = x + y.  Again, complete the calculation yourself.