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: Define the variable

Let \( x \) be the number of text messages. The monthly cost is a fixed \$20 plus \$0.10 per text message, so the total cost is \( 20 + 0.10x \). She doesn't want to spend more than \$40, so the inequality is \( 20 + 0.10x \leq 40 \).

Step2: Solve the inequality

Subtract 20 from both sides: \( 0.10x \leq 40 - 20 \)
Simplify: \( 0.10x \leq 20 \)
Divide both sides by 0.10: \( x \leq \frac{20}{0.10} = 200 \)

Answer:

D. \( 20 + 0.10x \leq 40 \); She can send 200 text messages.