221k views
1 vote
One month Rachel rented 2 movies and 6 video games for a total of 42 . The next month she rented 5 movies and 3 video games for a total of 30 . Find the rental cost for each movie and each video game.

User Fogus
by
7.9k points

1 Answer

4 votes

Answer:

$2.25 and $6.25

Explanation:

To find the rental cost for each movie and each video game, we can set up a system of equations based on the given information.

Let's assume the rental cost for each movie is "m" and the rental cost for each video game is "v".

From the first month's rental, we have the equation:

2m + 6v = 42

From the second month's rental, we have the equation:

5m + 3v = 30

To solve this system of equations, we can use the method of substitution or elimination.

Method 1: Substitution

Step 1: Solve one equation for one variable in terms of the other variable.

From the first equation, we can solve for m:

2m = 42 - 6v

m = (42 - 6v) / 2

m = 21 - 3v

Step 2: Substitute the expression for m in the second equation.

5(21 - 3v) + 3v = 30

Step 3: Simplify and solve for v.

105 - 15v + 3v = 30

-12v = -75

v = 75 / 12

v ≈ 6.25

Step 4: Substitute the value of v back into either equation to solve for m.

Using the first equation:

2m + 6(6.25) = 42

2m + 37.5 = 42

2m = 42 - 37.5

2m = 4.5

m = 4.5 / 2

m = 2.25

Method 2: Elimination

Step 1: Multiply the first equation by 5 and the second equation by 2 to eliminate the m variable.

10m + 30v = 210

10m + 6v = 60

Step 2: Subtract the second equation from the first equation to eliminate the m variable.

(10m + 30v) - (10m + 6v) = 210 - 60

24v = 150

v = 150 / 24

v ≈ 6.25

Step 3: Substitute the value of v back into either equation to solve for m.

Using the first equation:

2m + 6(6.25) = 42

2m + 37.5 = 42

2m = 42 - 37.5

2m = 4.5

m = 4.5 / 2

m = 2.25

Therefore, the rental cost for each movie is approximately $2.25 and the rental cost for each video game is approximately $6.25.

User Jgthms
by
9.1k points

No related questions found