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] 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]

To find which inequalities represent the situation for Miguel's music purchases, let's break it down step by step:

1. Understand the Problem: Miguel has a [tex]$25 gift card to use. Each song costs $[/tex]1.50. Additionally, there is a [tex]$1.00 account activation fee.

2. Define Variables: Let $ m $ be the number of songs Miguel can buy.

3. Formulate the Cost Equation:
- The total cost Miguel has to pay is the sum of the account activation fee and the cost of the songs he buys.
- $\text{Total Cost} = \$[/tex]1.00 + \[tex]$1.50 \times m$.

4. Set Up the Inequality: Since Miguel cannot spend more than the $[/tex]25 on his gift card, the total cost should be less than or equal to [tex]$25.
- This gives us the inequality: $1 + 1.5m \leq 25$.

5. Rewriting the Inequality: The inequality can also be rearranged to show that $[/tex]25 is greater than or equal to the total cost.
- [tex]$25 \geq 1 + 1.5m$[/tex].

So, the two inequalities that correctly represent this situation are:
- [tex]$1 + 1.5m \leq 25$[/tex]
- [tex]$25 \geq 1 + 1.5m$[/tex]

These two options ensure that the combined cost of the activation fee and songs does not exceed the $25 on Miguel's gift card.