# 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? ##### 1 Answer Nov 1, 2015 7th minute #### Explanation: Let $p$be the price of the call Let $d$be the duration of the call The first company charges at a fixed rate. ${p}_{1} = 0.08 d$The second company charges differently for the first minute and succeeding minutes ${p}_{2} = 0.05 \left(d - 1\right) + 0.25$$\implies {p}_{2} = 0.05 d + 0.20$We want to know when will the charging of the second company be cheaper ${p}_{2} < {p}_{1}$$\implies 0.05 d + 0.20 < 0.08 d$$\implies 0.20 < 0.08 d - 0.05 d$$\implies 0.20 < 0.03 d$$\implies 100 \cdot 0.20 < 0.03 d \cdot 100$$\implies 20 < 3 d$$\implies d > 6 \frac{2}{3}$Since the companies both charge on a per-minute basis, we should round-up our computed answer $\implies d = 7\$

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