Yusuf is deciding between two different movie streaming sites to subscribe to. Plan A costs $16 per month plus $1.50 per movie watched. Plan B costs $20 per month plus $0.50 per movie watched. Let AA represent the monthly cost of Plan A if Yusuf watches xx per month, and let BB represent the monthly cost of Plan B if Yusuf watches xx movies per month. Write an equation for each situation, in terms of x, commax, and determine the number of monthly movies watched, x, commax, that would make the two plans have an equal monthly cost.

Question

Answer
Attempt 1 out of 2

A, equalsA=
B, equalsB=
Answer:

Answer 1

To determine the monthly costs of the two plans in terms of \( x \), where \( x \) represents the number of movies watched per month, we can write the equations for Plan A and Plan B as follows:

Plan A:

• Monthly cost = Monthly subscription + Cost per movie watched
• Monthly cost \( A \) can be expressed as: \[ A = 16 + 1.50x \]

Plan B:

• Monthly cost = Monthly subscription + Cost per movie watched
• Monthly cost \( B \) can be expressed as: \[ B = 20 + 0.50x \]

Now, we want to find the number of monthly movies watched \( x \) that makes the costs of the two plans equal. To do this, we can set the equations equal to each other: \[ 16 + 1.50x = 20 + 0.50x \]

Next, we can solve for \( x \):

1. Subtract \( 0.50x \) from both sides: \[ 16 + 1.50x - 0.50x = 20 \] which simplifies to: \[ 16 + 1.00x = 20 \]

2. Subtract 16 from both sides: \[ 1.00x = 20 - 16 \] which simplifies to: \[ 1.00x = 4 \]

3. Divide both sides by 1: \[ x = 4 \]

Thus, the number of monthly movies watched \( x \) that would make the two plans have an equal monthly cost is: \[ \boxed{4} \]