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 monthly cost is a fixed \( \$20 \) plus \( \$0.10 \) per text message \( x \). She doesn't want to spend more than \( \$40 \). 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 \( 0.10 \):
\( x\leq\frac{20}{0.10}=200 \)

Answer:

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