Question

a cell phone provider offers a plan that costs $30 per month plus $0.10 per text message sent or received. a comparable plan costs $50 per month but offers unlimited text messaging. complete parts a. and b. below.
a. how many text messages would have to be sent or received in order for the plans to cost the same each month?
in order for the plans to cost the same, 200 text messages would have to be sent or received.
(simplify your answer. type an integer or a decimal.)
b. if you send or receive an average of 50 text messages each month, which plan would you choose? why?
the plan with because than text messages are sent or received each month.

Explanation:

Step1: Set up cost equations

Let \(x\) be the number of text messages.
For the first plan (costs \(30 + 0.1x\)).
For the second plan (costs \(50\)).

Step2: Solve for \(x\) when costs are equal

Set \(30+0.1x = 50\).
Subtract \(30\) from both sides: \(0.1x=50 - 30\).
So, \(0.1x = 20\).
Divide both sides by \(0.1\): \(x=\frac{20}{0.1}=200\).

Step3: Evaluate for \(x = 50\)

For the first plan: \(30+0.1\times50=30 + 5=35\).
For the second plan: \(50\).

Answer:

a. \(200\) text messages.
b. Choose the first plan (costs \(30 + 0.1x\)). Because when \(x = 50\), the first - plan costs \(35\) and the second - plan costs \(50\). So the first plan is cheaper.