Your cell phone plan costs $39.99 per month plus $.15 for each text message you send or receive. You have at most $45 to spend on your cell phone bill. What is the maximum number of text messages that you can send or receive next month?
-What information do you know? What information do you need?
-What inequality can you use to find the maximum number of text messages that you can send or receive?
-What are the solutions of the inequality? Are they reasonable?

We know the cost per month for the plan and the cost per text, and we also know the amount we can afford to spend per month; we need to know the number of text messages we can send; the inequality 0.15t+39.99≤45 can be used to represent this situation; and the solution is t≤33, and it is reasonable.

Explanation:

Let t represent the number of text messages we can send. We know that each text message costs $0.15; this gives us the expression 0.15t. We also know that the plan costs $39.99 per month; this gives us a total cost of 0.15t+39.99. We know that we can afford to spend no more than $45 per month; since it is "no more than," this means we will use less than or equal to:

0.15t+39.99≤45

To solve this, first cancel the 39.99 by subtracting it from both sides:

0.15t+39.99-39.99 ≤ 45-39.99

0.15t ≤ 5.01

Divide both sides by 0.15:

0.15t/0.15 ≤ 5.01/0.15

t ≤ 33.4

We cannot send a portion of a text message, so we say that we can send no more than 33 text messages.