Question

Company A charges $10 per month for their streaming service and increases the cost by $2 for every additional feature. company B charges 15$ per month with a $1 for each added feature. Write linear equations for both companies and determine the point of intersection. interpret the shared solution in the context of the problem.

Answer 1

The equation for Company A is y = 10 + 2x, and for Company B it is y = 15 + x.

The point of intersection (5, 20) indicates that both companies will charge $20 for a service that includes 5 additional features.

Step-by-step explanation:

To write the linear equations for Company A and Company B, we will let x represent the number of additional features and y represent the total monthly cost.

For Company A, the base price is $10, and each additional feature adds $2 to the monthly cost. Therefore, the equation for Company A is y = 10 + 2x.

For Company B, the base price is $15, with each extra feature adding $1 to the monthly cost, resulting in the equation y = 15 + x.

To find the point of intersection, we set the two equations equal to each other and solve for x:

10 + 2x = 15 + x

2x - x = 15 - 10

x = 5

After finding the value of x, we substitute it back into either of the original equations to find the value of y:

y = 10 + 2(5) = $20

Now we have the point of intersection, which is (5, 20). This means that both companies will charge the same amount, $20, when customers subscribe to 5 additional features.