A movie streaming service charges a set fee for
membership each month, plus an additional fee
for the number of movies streamed each
month. If 2 movies are streamed, the cost is
$14 per month, however if 6 movies are
streamed, the cost is $20. Write an equation to
model the cost, y, based on the number of
movies streamed x.
We can start by setting up a system of two equations, one for each scenario:
When 2 movies are streamed:
y = a + bx
14 = a + 2b
When 6 movies are streamed:
y = a + bx
20 = a + 6b
Now we can solve for a and b by using either substitution or elimination. Let's use elimination:
Multiplying the first equation by -3:
-42 = -3a - 6b
Multiplying the second equation by 2:
40 = 2a + 12b
Adding the two equations:
-2 = -a + 6b
Solving for a:
a = 6b + 2
Now we can substitute this expression for a into one of the original equations (let's use the first one):
14 = (6b + 2) + 2b
Solving for b:
12 = 8b
b = 1.5
Finally, we can substitute both values of a and b into the equation for y:
y = (6b + 2) + bx
y = 6(1.5) + 2x
y = 9 + 2x
Therefore, the equation to model the cost based on the number of movies streamed is:
y = 9 + 2x
To write an equation to model the cost, we need to determine the relationship between the number of movies streamed and the cost per month.
Let's break down the problem:
- When 2 movies are streamed, the cost is $14 per month.
- When 6 movies are streamed, the cost is $20 per month.
To find the additional cost per movie streamed, we can subtract the base fee from the total cost:
Additional cost per movie = Total cost - Base fee
Let's calculate the additional cost per movie:
Additional cost per movie = $20 - $14 = $6
Now we can write the equation to model the cost:
y = (additional cost per movie * x) + base fee
In this case, the base fee is the cost when no movies are streamed, which is not mentioned. Assuming the base fee is $8 (since it is not provided in the problem), we can write the equation as:
y = 6x + 8
where:
y = cost per month
x = number of movies streamed