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Part A

A video streaming company offers two monthly plans.
Plan A: $3 per video viewed, plus a flat rate of $8 per month
Plan B: $5 per video viewed and no additional flat rate

A. Write an inequality to determine when the cost of viewing n videos using Plan A is less than the cost of viewing n videos using Plan B.


Choose...

Choose...

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Part B

Plan A is less expensive when
Choose...
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1 Answer

2 votes

Greetings from Brasil...

Let Ca be the function for Plan A and Cb the function for Plan B.

According to the problem statement, we can conclude that:

Ca(n) = 3n + 8

Cb(n) = 5n

where C is the cost and n is the number of videos

Cost that the user will pay for having watched n videos

Ca = cost of Plan A

Cb = cost of Plan B

Is there any point (n) that Ca will be equal to Cb??? Let's equate the functions to check if there is a common point and if there is, what would it be.

Ca = Cb

3n + 8 = 5n

2n = 8

n = 4

In n = 4 we have a condition for the cost that does not matter Ca or Cb.

I will present 2 ways to solve:

1 - building the graph of the functions and observing the points where the Y axis (cost axis) its smaller

2 - assigning 2 points - below n = 4 and above n = 4 - to observe the cost behavior

1 - see attachment

2 - let's choose the points n = 1 and n = 10 (as already said, n=4 does not matter Ca or Cb - meeting point / intersection point)

n = 1

Ca(1) = 3.1 + 8 = 11

Cb(1) = 5.1 = 5

Ca > Cb, then Cb better to the user

n = 10

Ca(10) = 3.10 + 8 = 38

Cb(10) = 5.10 = 50

Ca < Cb, then Ca better to the user

We can come to the following conclusion:

0 < n < 4 → better use Plan B (in this interval the cost to the user will be lower with Plan B)

n = 4 → It doesn't matter to use Plan A or Plan B.

n > 4 → better use Plan A (for n above 4 the cost to the user will be lower with Plan A)

Part A A video streaming company offers two monthly plans. Plan A: $3 per video viewed-example-1
User Thomas PEDOT
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