Question

jasmine is on a cell phone plan where she pays $20 a month plus $0.10 per text message. she does not want to spend more than $40 on her cell phone bill. write and solve the inequality that will tell her how many text messages she can send.
a 20 + 10x ≤ 40; she can send 2 text messages.
b 20 + 10x ≥ 40; she can send 2 text messages.
c 20 + 0.10x ≤ 40; she can send 20 text messages.
d 20 + 0.10x ≤ 40; she can send 200 text messages.

Explanation:

Step1: Set up the inequality

Let \(x\) be the number of text messages. The fixed cost is \(20\) dollars and the cost per text is \(0.10\) dollars. The total cost \(20 + 0.10x\) should be less than or equal to \(40\). So the inequality is \(20+0.10x\leq40\).

Step2: Solve the inequality for \(x\)

Subtract \(20\) from both sides:
\(20 + 0.10x-20\leq40 - 20\)
\(0.10x\leq20\)
Divide both sides by \(0.10\):
\(x=\frac{20}{0.10}=200\)

Answer:

D. \(20 + 0.10x\leq40\); She can send 200 text messages.