Given:
Paco's cell phone carrier charges him $0.20 for each text message he sends or receives, $0.15 per minute for calls, and a $15 monthly service fee. Paco is trying to keep his bill for the month below $30.
To Find:
The number of texts 't' Paco can send/receive in a month.
Answer:
[tex]0\leq t<75[/tex]
best describes the number of texts he can send or receive to keep his bill less than $30 in a month.
Step-by-step explanation:
Paco wants to keep is monthly bill below $30.
We see that he has to pay a foxed monthly service fee of $15. This means he is only left with a limit of $30 - $15 = $15 for his monthly calls and texts.
That is, the amount he has to pay for texting and calling has to be less than $15.
For texts, the cell phone carrier charges $0.20 for sending/receiving texts.
For calls, he is charged $0.15 per minute.
Let the number of text messages Paco can send or receive in a month be denoted by 't'.
Let the number of minutes Paco can call in a month be denoted by 'c'.
Then, the total cost of text messages he can send or receive per month would be 0.20t and the total cost of the minutes he spends on calls would be 0.15c. Together, the sum of these has to be less than $15 if his monthly bill has to be kept less than $30 (accounting for the monthly service fee).
So,
[tex]0.20t+0.15c<15[/tex]
The number of texts he can send will dpend on the number of minutes he spends on his calls. For Paco to spend maximum number of texts, he has to spend 0 minutes on calls.
So, putting c = 0, the aboce equation can be written as
[tex]0.20t+0<15\\\\0.20t<15\\\\t<75[/tex]
That is, Paco has to send and receive less than 75 texts.
So,
[tex]0\leq t<75[/tex]
best describes the number of texts he can send or receive to keep his bill less than $30 in a month.
