Question

An Internet service provider allows a certain number of free hours each month and then charges for each additional hour used. Wells, Ted, and Vino each have separate accounts. This month the total hours used by Wells and Ted was 105, and each used all of their free hours. Their total cost was $\$10$. Vino used 105 hours by himself and had to pay $\$26$. What is the number of cents charged for each extra hour

Answer 1

To find the cost charged for each extra hour, we can set up a system of equations using the given information. By solving these equations, we can determine the value of the number of free hours provided (A) and the cost charged for each extra hour (z).

Step-by-step explanation:

To find the cost charged for each extra hour, we need to set up a system of equations using the given information. Let:

• A = number of free hours provided
• x = hours used by Wells and Ted (105 hours in total)
• y = number of extra hours used by Wells and Ted
• z = cost charged for each extra hour
• w = hours used by Vino (105 hours)

From the given information, we can set up the following equations:

2A + zy = 10 (equation 1)

w + z(w-1) = 26 (equation 2)

Since Wells and Ted used all of their free hours (A), the number of extra hours used by them would be x-A (105-A). So, we can substitute y = 105-A in equation 1:

2A + z(105-A) = 10

Simplifying this equation, we get:

2A + 105z - zA = 10

Combining like terms:

A(2-z) + 105z = 10

Solving equation 2 for z:

z = (26-w)/(w-1)

Substituting this value of z in equation 3:

A(2 - (26-w)/(w-1)) + 105(26-w)/(w-1) = 10

Simplifying this equation will give us the value of A, and from there, we can find the value of z.

Answer 2

`P_(extra)=0.3 ($)/(hr)`

Step-by-step explanation:

Wells and Ted used 52.5 hr each (free hours) and paid 10$

Vino used 105 hr:

`H_(vino)=H_(free)+H_(extra)`

`H_(extra)=105-52.5=52.5 hr`

He paid 26$ (the 10$ of the free hours and 16$ for the extra):

`P_(extra)=(16$)/(52.5 hr)`

`P_(extra)=0.3 ($)/(hr)`