A cell phone company offers two different plans.
Plan A: Monthly fee of $28
30 free minutes
$0.45 per additional minute
Plan B: Monthly fee of $40
No free mins
$0.25 per additional minute
Determine the time in the mins that results in the same monthly cost for both plans.
28 + .45(n-30) = 40 + .25n
Solve for n.
1. One monthly phone plan costs $20 for 250 minutes of talk plus 10 cents for every text message. Another monthly plan offers 250 minutes for $30 plus 5 cents for every text message. Caroline expects to talk less than 250 minutes a month but will use the texting often. How many text messages will she need to send for both plans to cost the same?
To determine the time in minutes that results in the same monthly cost for both plans, we can set up an equation and solve for the unknown.
Let's denote the number of additional minutes used as "x".
For Plan A, the monthly cost is the sum of the monthly fee ($28) and the cost of additional minutes ($0.45 per additional minute). So the cost for Plan A can be expressed as:
Cost(A) = $28 + 0.45x
For Plan B, the monthly cost is the sum of the monthly fee ($40) and the cost of additional minutes ($0.25 per additional minute). So the cost for Plan B can be expressed as:
Cost(B) = $40 + 0.25x
We want to find the value of "x" that makes the monthly cost equal for both plans:
Cost(A) = Cost(B)
$28 + 0.45x = $40 + 0.25x
Let's simplify and solve for "x".
0.45x - 0.25x = $40 - $28
0.20x = $12
x = $12 / 0.20
x = 60
So, the time in minutes that results in the same monthly cost for both plans is 60 minutes.