Question

A phone company offers two monthly plans. Plan A costs

$14 plus an additional $0.17 for each minute of calls. Plan B costs $21plus an additional $0.13 for each minute of calls.


For what amount of calling do the two plans cost the same?
minutes
What is the cost when the two plans cost the same?
$

Answer 1

175 minutes

$43.75

Explanation:

Let y = total cost

x = minutes

Plan A charges $0.17 per minute, so we multiply x by 0.17 like this: 0.17x

$14 is also already added on

y = 0.17x + 14

Plan B charges $0.13 per minute, so we multiply x by 0.13 like this: 0.13x

$21 is already added on

y = 0.13x + 21

Now we have to find where both x'es in both equations are the same

0.17x + 14 = 0.13x + 21

First, subtract 14 from both sides

0.17x + 14 = 0.13x + 21

- 14 - 14

0.17x = 0.13x + 7

Then subtract 0.13x from both sides

0.17x = 0.13x + 7

-0.13x -0.13x

0.04x = 7

Finally, divide both sides by 0.04

0.04x/0.04 = 7/0.04

x = 175

175 minutes of phone calls will need to be made on both plans for their costs to equal.

To find the price of those plans, we need to plug in the new x in one of the starting equations. We'll use the equation from Plan A.

y = 0.17(175) + 14

y = 29.75 + 14

y = 43.75

If both costs of the plans were to equal, they would cost $43.75