One cell phone company charges $0.08 a minute per call. Another cell phone company charges $0.25 for the first minute and $0.05 a minute for each additional minute. At what point will the second phone company be cheaper?

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Answer 1 · 2015-11-01T09:02:25

7th minute

Let #p# be the price of the call
Let #d# be the duration of the call

The first company charges at a fixed rate.

#p_1 = 0.08d#

The second company charges differently for the first minute and succeeding minutes

#p_2 = 0.05(d - 1) + 0.25#
#=> p_2 = 0.05d + 0.20#

We want to know when will the charging of the second company be cheaper

#p_2 < p_1#

#=> 0.05d + 0.20 < 0.08d#

#=> 0.20 < 0.08d - 0.05d#

#=> 0.20 < 0.03d#

#=> 100* 0.20 < 0.03d * 100#

#=> 20 < 3d#

#=> d > 6 2/3#

Since the companies both charge on a per-minute basis, we should round-up our computed answer

#=> d = 7#

Hence, the charging of the second company will be cheaper when the call duration exceeds 6 minutes (i.e. 7th minute).