A communications company offers a variety of calling card options. Card A has a 30¢ connection fee and then costs 2¢ per minute. Card B has a 10¢ connection fee and then costs 6¢ per minute. Find the length of the call that would cost the same with both cards.

The length of the call that would cost the same with both cards is 5 minutes.

Step-by-step explanation:

Hi there!

The cost with card A can be expressed as follows:

cost A = 30 + 2 · m

Where "m" is the length of the call in minutes.

In the same way, the cost of card B will be:

cost B = 10 + 6 · m

Where "m" is the length of the call in minutes.

We have to find the value of "m" for which the call would cost the same with both cards.

Then:

cost A = cost B

30 + 2 · m = 10 + 6 · m

Subtract 10 and 2 · m to both sides of the equation:

30 - 10 = 6 · m - 2 · m

20 = 4 · m

Divide by 4 both sides of the equation:

20/4 = m

5 = m

The length of the call that would cost the same with both cards is 5 minutes.

Have a nice day!