Answer :
Let's tackle the problem step by step!
We want to find the inequalities that represent the number of songs, [tex]\( m \)[/tex], Miguel can purchase with his [tex]$25 gift card.
1. Understanding the Costs:
- Each song costs $[/tex]1.50.
- There is a one-time account activation fee of [tex]$1.00.
2. Total Money Miguel Has:
Miguel has a total of $[/tex]25 on his gift card.
3. Setting Up the Inequality:
- The total cost of buying [tex]\( m \)[/tex] songs is represented by the expression: [tex]\( 1.00 + 1.50 \times m \)[/tex].
- Miguel can spend at most [tex]$25, so the expression \( 1.00 + 1.50 \times m \) should be less than or equal to 25. This gives us our first inequality:
\[
1 + 1.5m \leq 25
\]
4. Testing Total to be Strictly Less Than:
- Additionally, we consider the case where the total cost should be strictly less than $[/tex]25. This results in:
[tex]\[
1 + 1.5m < 25
\][/tex]
5. Form the Options as Inequalities:
- The two inequalities that accurately represent the situation are:
- [tex]\( 1 + 1.5m \leq 25 \)[/tex]
- [tex]\( 1 + 1.5m < 25 \)[/tex]
These inequalities define the maximum number of songs Miguel can purchase while considering the activation fee and the cost per song.
We want to find the inequalities that represent the number of songs, [tex]\( m \)[/tex], Miguel can purchase with his [tex]$25 gift card.
1. Understanding the Costs:
- Each song costs $[/tex]1.50.
- There is a one-time account activation fee of [tex]$1.00.
2. Total Money Miguel Has:
Miguel has a total of $[/tex]25 on his gift card.
3. Setting Up the Inequality:
- The total cost of buying [tex]\( m \)[/tex] songs is represented by the expression: [tex]\( 1.00 + 1.50 \times m \)[/tex].
- Miguel can spend at most [tex]$25, so the expression \( 1.00 + 1.50 \times m \) should be less than or equal to 25. This gives us our first inequality:
\[
1 + 1.5m \leq 25
\]
4. Testing Total to be Strictly Less Than:
- Additionally, we consider the case where the total cost should be strictly less than $[/tex]25. This results in:
[tex]\[
1 + 1.5m < 25
\][/tex]
5. Form the Options as Inequalities:
- The two inequalities that accurately represent the situation are:
- [tex]\( 1 + 1.5m \leq 25 \)[/tex]
- [tex]\( 1 + 1.5m < 25 \)[/tex]
These inequalities define the maximum number of songs Miguel can purchase while considering the activation fee and the cost per song.