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 . Vino used 105 hours by himself and had to pay . What is the number of cents charged for each extra hour

Answer 1

The internet service provider charges 40 cents for each extra hour used.

Also, he provides 40 hours of free service for every account.

Solved using linear equations.

Let the number of free hours provided by the internet service provider be x, and the charge for each extra hour be p cents.

Let the time consumed by Wells, Ted, and Vino be t1, t2, and t3 respectively.

Chargeable time used by Wells = t1 - x.

Cost for Wells = p(t1 - x).

Chargeable time used by Ted = t2 - x.

Cost for Ted = p(t2 - x).

Chargeable time used by Vino = t3 - x.

Cost for Vino = p(t3 - x).

Now, we are given that Wells and Ted, in total used 105 hours, that is, t1 + t2 = 105.

The cost for them together is $10 or 1000 cents.

This can be shown as the linear equation:

p(t1 - x) + p(t2 - x) = 1000.

or, p{(t1 - x) + (t2 - x)} = 1000,

or, p{(t1 + t2) - 2x} = 1000,

or, p(105 - 2x) = 1000,

or, p = 1000/(105 - 2x) ... (i).

Time consumed by Vino is given as 105 hours, thus, t3 = 105.

The total cost to Vino is given as $26 or 2600 cents.

This now can be shown as the linear equation:

p(t3 - x) = 2600,

or, {1000/(105 - 2x)}(105 - x) = 2600 {Substituting t3 = 105, and p = 1000/(105 - 2x)}.

This is the required linear equation in one variable.

It can be solved as follows:

{1000/(105 - 2x)}(105 - x) = 2600,

or, 105000 - 1000x = 273000 - 5200x,

or, 5200x - 1000x = 273000 - 105000,

or, 4200x = 168000,

or, x = 168000/4200 = 40.

Substituting x = 40 in (i), we get:

p = 1000/(105 - 2x),

or, p = 1000/(105 - 2(40)),

or, p = 1000/(105 - 80),

or, p = 1000/25,

or, p = 40.

Thus, the internet service provider charges 40 cents for each extra hour, and he provides 40 hours of free internet on every account.

The provided question is incomplete. The complete question is:

"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?"

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