algebra question

Question

A cell phone carrier charges a fixed monthly fee plus a constant rate for each minute used.

Part 1. In January, the total cost for 400 minutes was $53 while in February, the total cost for 225 minutes was $49.5 The constant charge for each minute used is:

1. 0.04
2. 0.02
3. 0.03

Part 2. The fixed montly fee charged by the carrier is;

Answer 1

Total Cost = (Fixed Monthly Fee) + (constant rate)(number of minutes)

Let "C" = Total Cost in dollars

Let "F" = Fixed Monthly Fee in dollars

Let "r" = constant rate in dollars per minute

Let "m" = the number of minutes used

So:

C = F + r•m

We are told that for January, C = 53 when m = 400 which makes the equation:

53 = F + 400r or F = 53 - 400r

And we are told that in February, C = 49.50 when m = 225 which makes the equation:

49.50 = F + 225r or F = 49.50 - 225r

Since F equals both "53 - 400r" and "49.50 - 225r" then "53 - 400r" must equal "49.50 - 225r"

53 - 400r = 49.50 - 225r

subtract 49.50 from both sides to get:

3.50 - 400r = -225r

Adding 400r to both sides gives us:

3.50 = 175r

Dividing both sides by 175 gives us:

r = 0.2

Now, using the fact that F = 53 - 400r, we can plug in r = 0.02 to get:

F = 53 - 400(0.02)

F = 53 - 8

F = 45

So the Fixed Monthly Fee is $45 and the constant rate is $0.02/minute