One month dale rented 8 movies and 4 video games for a total of $49. the next month he rented 3 movies and 2 video games for a total of $21 . find the rental cost for each movie and each video game.

Let, the rental cost for each movie = $x

And rental cost for each video game = $y

Dale rented 8 movies and 4 video games.

So rental cost for 8 movies = $(8x)

Rental cost for 4 video games = $(4y)

Given the total cost for 8 movies and 4 video games is $ 49

So we can write the equation as

8x+4y = 49equation 1

Dale next month rented 3 movies and 2 video games

Rental cost for 3 movies = $(3x)

Rental cost for 2 video games = $(2y)

Given the total cost for 3 movies and 2 video games = $21

So we can write the equation as,

3x+2y = 21 equation 2

From equation 2, we will find x in terms of y. So we will first move 2y to the other side by subtracting it.

3x = 21 - 2y

Now to get x from 3x, we will divide 3 to both sides,

3x/3 = (21-2y)/3

x = (21-2y)/3

We will plug in this value of x in equation 1 to get y.

8(21-2y)/3 + 4y = 49

(168-16y)/3 + 4y = 49

We have 3 in the denominator. To get rid of that denominator we will multiply both sides by 3.

3[(168-16y)/3 + 4y] = 3× 49

(168-16y) +12y = 147

168-16y+12y = 147

168 -4y = 147

We will move 168 to the right side now by subtracting it from both sides.

168 - 4y - 168 = 147 - 168

-4y = -21

To get y from -4y, we will divide both sides by -4.

(-4y)/(-4) = (-21)/(-4)

y = 21/4 = 5.25

We have got the value of y. By plugging in this value to equation 2, we will get x.

3x + 2y = 21

3x + 2(5.25) = 21

3x + 10.5 = 21

We will subtract 10.5 from both sides.

3x+10.5 - 10.5 = 21-10.5

3x = 10.5

To get x from 3x, we will divide both sides by 3.

3x/3 = 10.5/3

x = 3.5

We have got the required answers.

The rental cost for each movie is $3.5 and rental cost for each video game is $5.25.

:

step-by-step explanation: