Question

determining reasonable values

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. which best describes the possible values of t, the number of texts he can send or receive?

• t can be any real number where 0 ≤ t < 75.
• t can be any whole number where 0 ≤ t < 75.
• t can be any real number where 0 ≤ t < 150.
• t can be any whole number where 0 ≤ t < 150.

Explanation:

Step1: Set up the inequality

The total bill is the service fee plus the cost of texts. Let \( t \) be the number of texts. The cost for texts is \( 0.20t \), and the service fee is \( 15 \). We want the total bill to be below \( 30 \), so the inequality is \( 15 + 0.20t < 30 \).

Step2: Solve the inequality

Subtract \( 15 \) from both sides: \( 0.20t < 30 - 15 \) which simplifies to \( 0.20t < 15 \). Then divide both sides by \( 0.20 \): \( t < \frac{15}{0.20} = 75 \). Since the number of texts \( t \) must be a whole number (you can't send a fraction of a text), \( t \) is a whole number with \( 0 \leq t < 75 \).

Answer:

\( t \) can be any whole number where \( 0 \leq t < 75 \) (the second option).