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Answer :
To find which inequalities represent the situation for Miguel's music purchases, let's break it down step by step:
1. Understand the Problem: Miguel has a [tex]$25 gift card to use. Each song costs $[/tex]1.50. Additionally, there is a [tex]$1.00 account activation fee.
2. Define Variables: Let \( m \) be the number of songs Miguel can buy.
3. Formulate the Cost Equation:
- The total cost Miguel has to pay is the sum of the account activation fee and the cost of the songs he buys.
- \(\text{Total Cost} = \$[/tex]1.00 + \[tex]$1.50 \times m\).
4. Set Up the Inequality: Since Miguel cannot spend more than the $[/tex]25 on his gift card, the total cost should be less than or equal to [tex]$25.
- This gives us the inequality: \(1 + 1.5m \leq 25\).
5. Rewriting the Inequality: The inequality can also be rearranged to show that $[/tex]25 is greater than or equal to the total cost.
- [tex]\(25 \geq 1 + 1.5m\)[/tex].
So, the two inequalities that correctly represent this situation are:
- [tex]\(1 + 1.5m \leq 25\)[/tex]
- [tex]\(25 \geq 1 + 1.5m\)[/tex]
These two options ensure that the combined cost of the activation fee and songs does not exceed the $25 on Miguel's gift card.
1. Understand the Problem: Miguel has a [tex]$25 gift card to use. Each song costs $[/tex]1.50. Additionally, there is a [tex]$1.00 account activation fee.
2. Define Variables: Let \( m \) be the number of songs Miguel can buy.
3. Formulate the Cost Equation:
- The total cost Miguel has to pay is the sum of the account activation fee and the cost of the songs he buys.
- \(\text{Total Cost} = \$[/tex]1.00 + \[tex]$1.50 \times m\).
4. Set Up the Inequality: Since Miguel cannot spend more than the $[/tex]25 on his gift card, the total cost should be less than or equal to [tex]$25.
- This gives us the inequality: \(1 + 1.5m \leq 25\).
5. Rewriting the Inequality: The inequality can also be rearranged to show that $[/tex]25 is greater than or equal to the total cost.
- [tex]\(25 \geq 1 + 1.5m\)[/tex].
So, the two inequalities that correctly represent this situation are:
- [tex]\(1 + 1.5m \leq 25\)[/tex]
- [tex]\(25 \geq 1 + 1.5m\)[/tex]
These two options ensure that the combined cost of the activation fee and songs does not exceed the $25 on Miguel's gift card.
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