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Answer :
To determine which inequalities can represent the situation, let's break down the problem:
Miguel wants to buy songs with his [tex]$25 gift card. Each song costs $[/tex]1.50, and there's a [tex]$1.00 activation fee that he must pay regardless of how many songs he buys.
Let's represent:
- \( m \) as the number of songs Miguel can buy.
- Total cost as the sum of the activation fee and the cost of the songs (\$[/tex]1.50 per song).
### Step-by-step analysis:
1. Calculate the total cost:
The total cost for buying [tex]\( m \)[/tex] songs includes the activation fee and the cost of the songs:
[tex]\[
\text{Total cost} = 1 + 1.5m
\][/tex]
2. Set up the inequality for the gift card limit:
Miguel can spend at most \[tex]$25, which means the total cost must be less than or equal to \$[/tex]25:
[tex]\[
1 + 1.5m \leq 25
\][/tex]
3. Rephrase the inequality:
Alternatively, you can also think of it as checking if $25 is greater than the total cost:
[tex]\[
25 > 1 + 1.5m
\][/tex]
Based on this analysis, the inequalities that correctly represent the situation are:
1. [tex]\( 1 + 1.5m \leq 25 \)[/tex]
2. [tex]\( 25 > 1 + 1.5m \)[/tex]
These two inequalities correctly illustrate the conditions under which Miguel can use his gift card to buy the songs.
Miguel wants to buy songs with his [tex]$25 gift card. Each song costs $[/tex]1.50, and there's a [tex]$1.00 activation fee that he must pay regardless of how many songs he buys.
Let's represent:
- \( m \) as the number of songs Miguel can buy.
- Total cost as the sum of the activation fee and the cost of the songs (\$[/tex]1.50 per song).
### Step-by-step analysis:
1. Calculate the total cost:
The total cost for buying [tex]\( m \)[/tex] songs includes the activation fee and the cost of the songs:
[tex]\[
\text{Total cost} = 1 + 1.5m
\][/tex]
2. Set up the inequality for the gift card limit:
Miguel can spend at most \[tex]$25, which means the total cost must be less than or equal to \$[/tex]25:
[tex]\[
1 + 1.5m \leq 25
\][/tex]
3. Rephrase the inequality:
Alternatively, you can also think of it as checking if $25 is greater than the total cost:
[tex]\[
25 > 1 + 1.5m
\][/tex]
Based on this analysis, the inequalities that correctly represent the situation are:
1. [tex]\( 1 + 1.5m \leq 25 \)[/tex]
2. [tex]\( 25 > 1 + 1.5m \)[/tex]
These two inequalities correctly illustrate the conditions under which Miguel can use his gift card to buy the songs.
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