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 $ 20.94Solution: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 = 4.32a = 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