To find the maximum number of minutes [tex]\( m \)[/tex] that a person can talk on a long-distance telephone call without the cost exceeding [tex]$3, we need to set up an inequality based on the given cost structure.
1. The cost for the first minute of the call is $[/tex]0.35.
2. Each additional minute costs [tex]$0.10.
3. The total cost must not exceed $[/tex]3.
The cost structure can be broken down as follows:
- First minute: [tex]$0.35
- Each additional minute: $[/tex]0.10
To set up the inequality, let [tex]\( m \)[/tex] represent the total number of minutes the call lasts. The cost of the call can be calculated as:
[tex]\[ \text{Cost of the call} = 0.35 + 0.10 \times (m - 1) \][/tex]
Here, [tex]\( (m - 1) \)[/tex] represents the number of additional minutes after the first minute.
The total cost must be less than or equal to [tex]$3, so we have:
\[ 0.35 + 0.10(m - 1) \leq 3 \]
Now, let's simplify this inequality step-by-step:
1. Distribute the 0.10:
\[ 0.35 + 0.10m - 0.10 \leq 3 \]
2. Combine the constants:
\[ 0.25 + 0.10m \leq 3 \]
3. Subtract 0.25 from both sides of the inequality:
\[ 0.10m \leq 2.75 \]
4. Divide both sides by 0.10 to solve for \( m \):
\[ m \leq \frac{2.75}{0.10} \]
\[ m \leq 27.5 \]
Since \( m \) must be a whole number (as we can't talk for a fraction of a minute in this context), the maximum integer value for \( m \) is 27.
Therefore, the inequality representing the number of minutes \( m \) a person can talk without exceeding $[/tex]3 is:
[tex]\[ m \leq 27 \][/tex]
None of the provided answer choices explicitly state "m \leq 27." However, given this derived solution:
The correct answer is:
```
d. None of the above
```
