Question

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.

Answer 1

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 = 49.....equation 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.

Answer 2

Alright, lets get started.

Lets suppose, the cost of each movie = m

Hence cost of 8 movies will be = 8 m

And, lets suppose cost of each video game = v

Hence cost of 4 video games will be = 4 v

8 movies and 4 video games for a total of $49 (as given in question)

8 m + 4 v = 49...................................Equation (1)

The next month he rented 3 movies and 2 video games.

Cost of 3 movies will be 3 m and cost of 2 video games will be 2v.

3m + 2 v = 21

Multiplying this with 2

6m + 4 v = 42 ...................................Equation (2)

Subtracting equation (1) and equation (2)

8m + 4v - 6m - 4v = 49 - 42

2m = 7

Dividing both sides with 2

2m / 2 = 7 / 2

m = 3.5 $

Putting the value of m in equation (1)

8 m + 4 v = 49

8 * 3.5 + 4 v = 49

28 + 4 v = 49

4 v = 21

Dividing both sides with 4

4 v / 4 = 21 / 4

v = 5.25 $

Hence rental cost of each movie is 3.5 $ and video game is 5.25 $. : Answer

Hope it will help :)