Question

One cellular phone carrier charges 26.50 a month plus .15cents a minute. Another carrier charges 14.50 a month plus .25 cents a minute. For how many minutes is the cost of the plans the same? Please show work thanks

Answer 1

I'm going to use m for minutes
Cell carrier 1
0.15 per minute (0.15m)
$26.50 first, and then add on for every minute

cost carrier 1 = 0.15m + 26.50

carrier 2
0.25 per minute (0.25m)
$14.50 first, and then add on for every minute. 

cost carrier 2 = 0.25m + 14.50 

to find out when they cost the same, make the two costs equal to each other:

0.15m + 26.50 = 0.25m + 14.50

all that's left is to solve for m

0.15m + 26.50 = 0.25m + 14.50
subtract both sides by 0.15 m
26.50 = 0.2m + 14.50
subtract both sides by 14.50
12 = 0.1 m 
divide both sides by 0.1
m = 120

the phone carriers will have the same cost at 120 minutes

Answer 2

Define the rates of each carrier:

(1) $26.50 + $0.15m
(2) $14.50 + $0.25m

Set the two equations equal to each other and solve for m minutes . . .

26.50 + 0.15m = 14.50 + 0.25m

26.50 - 14.50 = 0.25m - 0.15m

12.00 = (0.25 - 0.15)m

12 = 0.10m

m = 12/0.10 = 120

m = 120 minutes