Question

Video streaming company A charges a one-time $40 membership fee and $2 per video stream. Video streaming company B charges a one-time $20 membership fee and $4 per video stream.
Let the variable s represent the amount of videos streamed and let the variable c represent the cost.

For how many video streams will the cost be the same for both companies?

Which system of equations can be used to solve this problem?



{c=40s+2
c=20s+4

{c=40+2s
c=20+4s

{c=42s
c=24s

{c=40−2s
c=20−4s

Answer 1

Let's begin ! ^_^

You have got informations in your problem that you just have to translate in a "mathematic language".

Company A :
"$40 membership fee and $2 per video stream."

Thanks to that, you can guess :
c = 40 + 2s

Now let's do the same thing to the company B.

Company B :
"charges a one-time $20 membership fee and $4 per video stream."

Therefore, c = 20 + 4s.

I think you have guessed !! =D And yes the system of equation that you have to solve and you're looking for is :

{c=40+2s ( Option B)
c=20+4s.

Second step : For how many video streams will the cost be the same for both companies?

We just have to solve the system :) And there is only one variable, the letter "s".

We know that we have to find equal costs as it is said in the question " the cost be the same for both companies", so :

=> 40 + 2s = 20 +4s
=> 4s - 2s = 40 - 20
=> 2s = 20
=> s = 20/2
=> s = 10

Verification :

Company A :
=> 40 + 2s = 40 + 2*10 = 40 + 20 =60.

Company B :

=> 20 + 4s = 20 + 4*10 = 20 + 40 = 60

As you have seen, the costs are the same for both companies.

We can say that as a conclusion for 10 video streams, the cost will be the same for both companies.

In short, the answer would be : 10.

Let me give you an advice : Usually the word "per" means a multiplication is the mathematic language.

Hope this helps !

Photon