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.
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 :)
