Answer :
Let's break down the problem step by step to determine which inequalities represent the situation where Miguel uses his [tex]$25 gift card for purchasing songs.
1. Understand the costs involved:
- There's a one-time account activation fee of $[/tex]1.00.
- Each song costs [tex]$1.50.
2. Set up the inequality:
- Miguel wants to buy `m` songs with his gift card worth $[/tex]25.
- The total cost will include the activation fee and the cost for the songs:
[tex]\[
\text{Total Cost} = \$1.00 + \$1.50 \times m
\][/tex]
- This total cost should not exceed the value of the gift card:
[tex]\[
1 + 1.5m \leq 25
\][/tex]
3. Look for inequalities that align with this setup:
- The inequality [tex]\(1 + 1.5m \leq 25\)[/tex] directly represents our condition, meaning Miguel cannot spend more than the [tex]$25 gift card.
- Rewriting the inequality, we have:
\[
1 + 1.5m < 25 + \text{(if he doesn’t use the whole card)}
\]
- This allows for the possibility that Miguel spends less than the total $[/tex]25 value.
4. Select the correct options:
Based on the above reasoning, the two inequalities that correctly represent the situation are:
- [tex]\(1+1.5m \leq 25\)[/tex]
- [tex]\(1+1.5m < 25\)[/tex]
These inequalities ensure that the total spent, including both the activation fee and the cost of songs, does not exceed or exactly matches the gift card value.
1. Understand the costs involved:
- There's a one-time account activation fee of $[/tex]1.00.
- Each song costs [tex]$1.50.
2. Set up the inequality:
- Miguel wants to buy `m` songs with his gift card worth $[/tex]25.
- The total cost will include the activation fee and the cost for the songs:
[tex]\[
\text{Total Cost} = \$1.00 + \$1.50 \times m
\][/tex]
- This total cost should not exceed the value of the gift card:
[tex]\[
1 + 1.5m \leq 25
\][/tex]
3. Look for inequalities that align with this setup:
- The inequality [tex]\(1 + 1.5m \leq 25\)[/tex] directly represents our condition, meaning Miguel cannot spend more than the [tex]$25 gift card.
- Rewriting the inequality, we have:
\[
1 + 1.5m < 25 + \text{(if he doesn’t use the whole card)}
\]
- This allows for the possibility that Miguel spends less than the total $[/tex]25 value.
4. Select the correct options:
Based on the above reasoning, the two inequalities that correctly represent the situation are:
- [tex]\(1+1.5m \leq 25\)[/tex]
- [tex]\(1+1.5m < 25\)[/tex]
These inequalities ensure that the total spent, including both the activation fee and the cost of songs, does not exceed or exactly matches the gift card value.
