We are given two companies with different pricing structures:

• Company A charges a one-time membership fee of $40 and $2 per video stream.
• Company B charges a one-time membership fee of $20 and $4 per video stream.

Let:

• $s$ represent the number of streamed videos.
• $c$ represent the total cost charged by each company.

Step 1: Set up the system of equations

For Company A: $c_A = 40 + 2s$ For Company B: $c_B = 20 + 4s$

We want to find the value of $s$ (number of streamed videos) when both companies charge the same total amount. Therefore, we set $c_A = c_B$: $40 + 2s = 20 + 4s$

Step 2: Solve the equation

Now, solve for $s$:

1. Subtract $2s$ from both sides: $40 = 20 + 2s$

2. Subtract 20 from both sides: $20 = 2s$

3. Divide by 2: $s = 10$

Conclusion

The two companies will charge the same total amount when 10 videos are streamed.

Would you like more details or have any questions?

Here are 5 related questions:

1. How much does each company charge after 10 video streams?
2. For how many videos will Company A be cheaper than Company B?
3. For how many videos will Company B be cheaper than Company A?
4. What is the total cost for 15 streams from each company?
5. How would the system change if Company B charged $3 per stream instead?

Tip: When dealing with linear equations, solving for equality (like in this example) often helps identify points of intersection or comparison.