The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 47 minutes of calls is $18.90 and the monthly cost for 83 minutes is $23.22. What is the monthly cost for 64 minutes of calls?

The monthly cost for 64 minutes of calls is $ 20.94

Solution:

Given, The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes).

Let it be, m = an + b

Where, m is monthly cost, a is cost per minute, n is number of minutes of call, and b is initial charges.

The monthly cost for 47 minutes of calls is $18.90

Then, 18.9 = 47a + b ⇒ (1)

And the monthly cost for 83 minutes is $23.22.

Then, 23.22 = 83a + b ⇒ (2)

Now, subtract (1) from (2)

36a = 4.32

a = 0.12

Now substitute a value in (1)

47 (0.12) + b = 18.9

b = 18.9 - 5.64

b = 13.26

Then, our equation becomes m = 0.12n + 13.26 - - - eqn (3)

We have to find what is the monthly cost for 64 minutes of calls?

So, substitute n = 64 in (3)

m = 0.12 x 64 + 13.26

m = 7.68 + 13.26 = 20.94

Hence, the cost is $ 20.94 for 64 minutes of call