A cell phone provider ofers a plan that costs $20 per month plus 80,20 per text message sent or recelved. A comparable plan costs 850 per month but offers unlimited tex messaging. Complete parts a. and b. below.
a) Define a variable to represent the number of text messages sent or received and write an equation to represent the cost of the first cell phone provider's plan in terms of the variable.
Let's say the variable x represents the number of text messages sent or received. The cost of the first cell phone provider's plan can be represented by the equation:
Cost(x) = $20 + $0.20x
b) Determine the number of text messages for which the first cell phone provider's plan is a better deal than the comparable plan.
To find the number of text messages, x, for which the first cell phone provider's plan is a better deal, we need to compare the costs of the two plans.
For the comparable plan with unlimited text messaging, the cost is $850 per month.
So we need to find x for which:
$20 + $0.20x < $850
Simplifying:
$0.20x < $830
x < 830 / 0.20
x < 4150
Therefore, for any number of text messages less than 4150, the first cell phone provider's plan is a better deal.