Answer:
Step-by-step 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:
\(charge_A(t)= 35 \ c + 3 \ \frac{c}{min} * t\)
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:
\(charge_B(t)= 45 \ c + 2 \ \frac{c}{min} * t\).
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:
\(35 \ c + 3 \ \frac{c}{min} * t'= 45 \ c + 2 \ \frac{c}{min} * t'\)
doing a little work...
\(35 \ c + 3 \ \frac{c}{min} * t' - 35 \ c = 45 \ c + 2 \ \frac{c}{min} * t' - 35 \ c\)
\(3 \ \frac{c}{min} * t'= 10 \ c + 2 \ \frac{c}{min} * t'\)
\(3 \ \frac{c}{min} * t' - 2 \ \frac{c}{min} * t'= 10 \ c\)
\(1 \ \frac{c}{min} * t'= 10 \ c\)
\(\frac{1 \ \frac{c}{min} * t'}{1 \ \frac{c}{min}}= \frac{10 \ c}{1 \ \frac{c}{min}}\)
\(t'= 10 min\)
And this is the length of time we are looking for.
