Question

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?

Answer 1

The correct answers are:

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.

Answer 2

No more than 33 texts a month
you know the total amount spent, you know the total of the bill without texts
45=39.99+.15t