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Answer :
To help Miguel decide how many songs he can purchase with his [tex]$25 gift card, we need to consider the cost per song and the one-time account activation fee.
1. Identify the Variables:
- The cost per song is $[/tex]1.50.
- The account activation fee is [tex]$1.00.
- Let \( m \) be the number of songs Miguel can buy.
- Miguel's total budget is $[/tex]25.
2. Create an Inequality to Represent the Situation:
- The total cost includes the activation fee plus the cost of [tex]\( m \)[/tex] songs.
- Total Cost = Activation Fee + Cost of Songs
- Mathematically, this is expressed as: [tex]\( 1 + 1.5m \)[/tex]
3. Ensure the Total Cost Does Not Exceed the Gift Card Amount:
- The total cost should be less than or equal to [tex]$25. This can be expressed as:
\[
1 + 1.5m \leq 25
\]
4. Express the Inequality in Different Forms:
- We can also express this inequality by changing the order but maintaining the same meaning. This gives us:
\[
25 \geq 1 + 1.5m
\]
So, the two inequalities that correctly represent the situation are:
- \( 1 + 1.5m \leq 25 \)
- \( 25 \geq 1 + 1.5m \)
These inequalities show the condition that Miguel's total expenditure for songs and the account activation fee should not exceed $[/tex]25.
1. Identify the Variables:
- The cost per song is $[/tex]1.50.
- The account activation fee is [tex]$1.00.
- Let \( m \) be the number of songs Miguel can buy.
- Miguel's total budget is $[/tex]25.
2. Create an Inequality to Represent the Situation:
- The total cost includes the activation fee plus the cost of [tex]\( m \)[/tex] songs.
- Total Cost = Activation Fee + Cost of Songs
- Mathematically, this is expressed as: [tex]\( 1 + 1.5m \)[/tex]
3. Ensure the Total Cost Does Not Exceed the Gift Card Amount:
- The total cost should be less than or equal to [tex]$25. This can be expressed as:
\[
1 + 1.5m \leq 25
\]
4. Express the Inequality in Different Forms:
- We can also express this inequality by changing the order but maintaining the same meaning. This gives us:
\[
25 \geq 1 + 1.5m
\]
So, the two inequalities that correctly represent the situation are:
- \( 1 + 1.5m \leq 25 \)
- \( 25 \geq 1 + 1.5m \)
These inequalities show the condition that Miguel's total expenditure for songs and the account activation fee should not exceed $[/tex]25.
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