One cellular phone carrier charges $26.50 a month and $0.15 a minute for local calls. Another carrier charges $14.50 a month and $0.25 per minute for local calls. For how many minutes is the cost of the plans the same?
difference is 12 dollars per month
so for them to be the same the 0.15 needs to catch up to 0.25 by 12 dollars
12 / 0.25-0.15 = 12 / 0.1 = 120 minutes
To find the number of minutes for which the cost of the plans is the same, we need to set up an equation and solve for the unknown variable.
Let's assume the number of minutes is represented by 'm'.
For the first carrier, the monthly cost is $26.50 plus the cost of each minute, which is $0.15m.
So the monthly cost for the first carrier is 26.50 + 0.15m.
For the second carrier, the monthly cost is $14.50 plus the cost of each minute, which is $0.25m.
So the monthly cost for the second carrier is 14.50 + 0.25m.
We want to find when the cost of the plans is the same, so we can set the two expressions equal to each other.
26.50 + 0.15m = 14.50 + 0.25m
Next, we can solve this equation for 'm' to determine the number of minutes.
First, let's isolate 'm' terms on one side of the equation and the constants on the other side:
0.15m - 0.25m = 14.50 - 26.50
-0.10m = -12
Now, divide both sides of the equation by -0.10 to solve for 'm':
m = (-12) / (-0.10)
m = 120
So, the cost of the plans will be the same for 120 minutes.