Question

the charges for an international call made using the calling card for two phone companies are shown in the table. what is the length of a phone call that would cost the same no matter witch company is used?

Answer 1

10 minutes would be your answer. I just solved for 35 + 3x=45+2x

Answer 2

• 10 minutes.

Explanation:

We can express the charge made by the companies as equations.

The charge made by the Company A starts at 35 cents, and cost 3 additional cents per minute. We can write this as:

`charge_A(t)= 35 \ c + 3 \ (c)/(min) * t`

where t is the length of the call in minutes. For the company B the charge starts at 45 cents, and cost 2 additional cents per minute. This is:

`charge_B(t)= 45 \ c + 2 \ (c)/(min) * t`.

Now. At what length t' the cost of the phone call is the same? We can write the condition as:

`charge_A(t')= charge_B(t')`

this means:

`35 \ c + 3 \ (c)/(min) * t'= 45 \ c + 2 \ (c)/(min) * t'`

doing a little work...

`35 \ c + 3 \ (c)/(min) * t' - 35 \ c = 45 \ c + 2 \ (c)/(min) * t' - 35 \ c`

`3 \ (c)/(min) * t'= 10 \ c + 2 \ (c)/(min) * t'`

`3 \ (c)/(min) * t' - 2 \ (c)/(min) * t'= 10 \ c`

`1 \ (c)/(min) * t'= 10 \ c`

`(1 \ (c)/(min) * t')/(1 \ (c)/(min))= (10 \ c)/(1 \ (c)/(min))`

`t'= 10 min`

And this is the length of time we are looking for.