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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]

Answer :

To solve the problem of determining how many songs Miguel can buy with his gift card, we need to consider the costs involved:

1. Activation Fee: There is a [tex]$1.00 fee for activating the account.
2. Cost per Song: Each song costs $[/tex]1.50.

Miguel has a total of [tex]$25 on his gift card to spend. We need to find inequalities that describe how many songs, \( m \), he can buy.

### Step-by-Step Explanation:

1. Calculate the Total Cost:
- The total cost to buy \( m \) songs is composed of the activation fee plus the cost of the songs.
- Total cost formula: \( \text{Activation Fee} + \text{Cost per Song} \times m = 1 + 1.5m \).

2. Set up Inequalities:
- Miguel cannot spend more than he has on the gift card, which is $[/tex]25. Therefore, we setup the inequalities:
- [tex]\( 1 + 1.5m \leq 25 \)[/tex]: This means the total cost (activation fee plus songs) should be less than or equal to [tex]$25.
- \( 1 + 1.5m < 25 \): This indicates the total cost should be less than $[/tex]25.

3. Other Inequalities to Consider:
- [tex]\( 25 > 1 + 1.5m \)[/tex]: This is another way to write [tex]\( 1 + 1.5m < 25 \)[/tex].
- [tex]\( 25 \geq 1 + 1.5m \)[/tex]: This is another way to express [tex]\( 1 + 1.5m \leq 25 \)[/tex].

### Options to Choose:
After analyzing, the correct inequalities that represent this situation are:

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

Both these inequalities correctly reflect the limitations Miguel has with his $25 gift card, considering the costs of the activation fee and the songs.

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