A phone plan has a limit of [tex]$25 that can be spent on text messages. The base cost of the text plan is $[/tex]5. Each text costs [tex]$0.05. How many text messages $[/tex](t)[tex]$ can a user send without exceeding the plan limits?

A. $[/tex]t \leq 400[tex]$
B. $[/tex]t < 400[tex]$
C. $[/tex]t \leq 600[tex]$
D. $[/tex]t < 600$



Answer :

Let's break down the problem step-by-step:

1. Understand the Total Limit:
The phone plan allows for a total expenditure of [tex]$25. 2. Account for the Base Cost: There is a base cost for the plan, which is $[/tex]5. This means [tex]$5 out of the $[/tex]25 will be used just for having the plan.

3. Calculate Remaining Money:
After paying the base cost, the amount of money left for text messages can be determined by subtracting the base cost from the total limit:
[tex]\[ 25 - 5 = 20 \][/tex]
So, there is [tex]$20 left to spend on text messages. 4. Determine the Cost per Text Message: Each text message costs $[/tex]0.05.

5. Calculate Maximum Number of Text Messages:
To find out how many text messages can be sent with the remaining $20, we divide the remaining money by the cost per text message:
[tex]\[ \frac{20}{0.05} = 400 \][/tex]

6. Interpret the Result:
The maximum number of text messages that can be sent without exceeding the plan limit is 400.

Thus, the answer is that a user can send up to 400 text messages. Therefore, the correct inequality describing this situation is:

[tex]\[ t \leq 400 \][/tex]

So, the correct option is:
[tex]\[ \boxed{t \leq 400} \][/tex]