Miguel can use all or part of his [tex]$\$25$[/tex] gift card to make a music purchase. Each song costs [tex]$1.50$[/tex], and there is a [tex]$\$1.00$[/tex] per account activation fee.

Which inequalities can represent this situation if [tex]m[/tex] is the number of songs he can buy? Select two options.

A. [tex]1 + 1.5m \leq 25[/tex]

B. [tex]1 + 1.5m \geq 25[/tex]

C. [tex]25 > 1 + 1.5m[/tex]

D. [tex]1 + 1.5m < 25[/tex]

E. [tex]25 \geq 1 + 1.5m[/tex]

Sure! Let's analyze the problem step by step to understand which inequalities are correct for determining how many songs Miguel can buy.

1. Identify the total amount Miguel can spend.
Miguel has a [tex]$25 gift card.

2. Understand the costs involved.
- Each song costs \$[/tex]1.50.
- There is an account activation fee of \[tex]$1.00.

3. Set up an inequality for the total cost.
If $ m $ is the number of songs Miguel buys, the total cost will be:

\[
\text{Total Cost} = 1.00 + 1.50m
\]

4. Determine the condition for the total cost.
The total cost $ 1.00 + 1.50m $ should be less than or equal to the \$[/tex]25 gift card amount.

So, the inequality is:

[tex]\[
1.00 + 1.50m \leq 25
\][/tex]

Additionally, since the total cost cannot exceed the gift card amount, it should also be strictly less than 25:

[tex]\[
1.00 + 1.50m < 25
\][/tex]

5. Compare with given options:
- [tex]$ 1 + 1.5m \leq 25 $[/tex]
- [tex]$ 1 + 1.5m \geq 25 $[/tex]
- [tex]$ 25 > 1 + 1.5m $[/tex]
- [tex]$ 1 + 1.5m < 25 $[/tex]
- [tex]$ 25 \geq 1 + 1.5m $[/tex]

Correct Inequalities:

- [tex]$ 1 + 1.5m \leq 25 $[/tex]
- [tex]$ 1 + 1.5m < 25 $[/tex]

These two inequalities correctly represent the situation where the total cost must be within the limit of the [tex]$\$[/tex] 25$ gift card. Therefore, they are the correct choices.

Final Answer:
- [tex]$ 1 + 1.5m \leq 25 $[/tex]
- [tex]$ 1 + 1.5m < 25 $[/tex]