Question

pacos 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. which best describes the possible values of t, the number of texts he can send or receive?
o t can be any real number where 0 ≤ t < 75.
o t can be any whole number where 0 ≤ t < 75.
o t can be any real number where 0 ≤ t < 150.
o t can be any whole number where 0 ≤ t < 150.

Explanation:

Step1: Set up the cost - inequality

Let's assume the number of minutes of calls is \(m\). The cost of texts is \(0.2t\), the cost of calls is \(0.15m\), and the monthly service fee is \(15\). The total cost \(C = 0.2t+0.15m + 15\). Since Paco wants to keep his bill below \(30\), we have the inequality \(0.2t+0.15m+15\lt30\). If we assume the minimum number of call - minutes (\(m = 0\)) (to find the maximum number of texts), the inequality becomes \(0.2t+15\lt30\).

Step2: Solve the inequality for \(t\)

Subtract \(15\) from both sides of the inequality \(0.2t+15\lt30\):
\(0.2t+15 - 15\lt30 - 15\), which simplifies to \(0.2t\lt15\).
Then divide both sides by \(0.2\): \(t\lt\frac{15}{0.2}=75\).
Also, the number of texts \(t\) cannot be negative, so \(t\geq0\). And the number of texts is a non - negative whole number (you can't send a fraction of a text).

Answer:

t can be any whole number where \(0\leq t\lt75\).