MaineCellular offers a phone plan that costs $12 per month plus 10 cents per minute. Portland Wireless offers a plan that costs $20 per month plus 5 cents per minute. How many minutes could you use in a month so that it would cost less to use the MaineCellular plan? Be specific in your answer - give the full range of minutes that answers the question.
X = the cost of MaineCellular's plan
P = the cost of Portland Wireless' plan
T = time in minutes.
X = $12 + $0.10 T
P = $20 + $0.05 T
P = X at the number of minutes that the two costs cross. So, set X = P
$12 + $0.10 T = $20 + $0.05 T
Solve for T.
Once you have T, anything less than T minutes will give one of the plans an edge. Which one?
Anything greater than T minutes will give the other plan the edge.
To determine how many minutes could be used in a month for it to cost less to use the MaineCellular plan, we need to find the point at which the cost of using the MaineCellular plan is equal to the cost of using the Portland Wireless plan.
Let's calculate the cost of using each plan for different amounts of minutes:
For the MaineCellular plan:
- Base cost: $12 per month
- Additional cost: 10 cents per minute
For the Portland Wireless plan:
- Base cost: $20 per month
- Additional cost: 5 cents per minute
Let's assume the number of minutes used in a month is represented by "m". The cost of the MaineCellular plan for m minutes is given by the equation:
Cost of MaineCellular = $12 + ($0.10 * m)
The cost of the Portland Wireless plan for m minutes is given by the equation:
Cost of Portland Wireless = $20 + ($0.05 * m)
To find the break-even point where both plans cost the same, we need to set these two equations equal to each other and solve for m:
$12 + ($0.10 * m) = $20 + ($0.05 * m)
We can simplify this equation:
$0.10 * m - $0.05 * m = $20 - $12
$6 * m = $8
m = $8 / $6
m = 4/3
Since we can't have a fractional number of minutes, we need to round up or down to the nearest whole number. In this case, since it is not possible to use a fraction of a minute, we will always round up.
Therefore, it would cost less to use the MaineCellular plan when using 2 or fewer minutes in a month. The full range of minutes that answers the question is 0 to 2 minutes.