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

The fixed cost is $20$ and the cost per text is $0.10$ dollars. Let $x$ be the number of text messages. The total cost is $20 + 0.10x$. She doesn't want to spend more than $40$, so the inequality is $20+0.10x\leq40$.

Step2: Solve the inequality

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.