Answer :
- The total cost of $m$ songs is $1 + 1.5m$.
- Since Miguel can use all or part of his $25 gift card, the total cost must be less than or equal to $25: $1 + 1.5m \leq 25$.
- This can also be written as $25 \geq 1 + 1.5m$.
- Since Miguel can use *all or part* of the gift card, the cost can also be strictly less than $25: $1 + 1.5m < 25$ and $25 > 1 + 1.5m$.
### Explanation
1. Understanding the Problem
Miguel has a $25 gift card to buy songs. Each song costs $1.5, and there's a $1 account activation fee. We need to find the inequalities that represent this situation, where $m$ is the number of songs he can buy.
2. Setting up the Inequality
The total cost of buying $m$ songs is the account activation fee plus the cost of the songs, which is $1 + 1.5m$. Since Miguel can use all or part of his $25 gift card, the total cost must be less than or equal to $25.
3. Expressing the Inequality
This gives us the inequality $1 + 1.5m
\leq 25$. We can also write this as $25
\geq 1 + 1.5m$.
4. Considering 'All or Part'
Since Miguel can use *all or part* of the gift card, the cost can also be strictly less than $25. This gives us the inequalities $1 + 1.5m < 25$ and $25 > 1 + 1.5m$.
5. Final Answer
Therefore, the inequalities that can represent this situation are:
$1+1.5 m \leq 25$
$25 \geq 1+1.5 m$
$25>1+1.5 m$
$1+1.5 m<25
### Examples
Imagine you're at a fair with a set amount on a prepaid card. This problem helps you figure out how many rides you can go on, considering the initial card fee and the cost per ride. Understanding these inequalities helps you manage your spending and make the most of your available funds. This is useful in budgeting, managing expenses, and making informed purchasing decisions.
- Since Miguel can use all or part of his $25 gift card, the total cost must be less than or equal to $25: $1 + 1.5m \leq 25$.
- This can also be written as $25 \geq 1 + 1.5m$.
- Since Miguel can use *all or part* of the gift card, the cost can also be strictly less than $25: $1 + 1.5m < 25$ and $25 > 1 + 1.5m$.
### Explanation
1. Understanding the Problem
Miguel has a $25 gift card to buy songs. Each song costs $1.5, and there's a $1 account activation fee. We need to find the inequalities that represent this situation, where $m$ is the number of songs he can buy.
2. Setting up the Inequality
The total cost of buying $m$ songs is the account activation fee plus the cost of the songs, which is $1 + 1.5m$. Since Miguel can use all or part of his $25 gift card, the total cost must be less than or equal to $25.
3. Expressing the Inequality
This gives us the inequality $1 + 1.5m
\leq 25$. We can also write this as $25
\geq 1 + 1.5m$.
4. Considering 'All or Part'
Since Miguel can use *all or part* of the gift card, the cost can also be strictly less than $25. This gives us the inequalities $1 + 1.5m < 25$ and $25 > 1 + 1.5m$.
5. Final Answer
Therefore, the inequalities that can represent this situation are:
$1+1.5 m \leq 25$
$25 \geq 1+1.5 m$
$25>1+1.5 m$
$1+1.5 m<25
### Examples
Imagine you're at a fair with a set amount on a prepaid card. This problem helps you figure out how many rides you can go on, considering the initial card fee and the cost per ride. Understanding these inequalities helps you manage your spending and make the most of your available funds. This is useful in budgeting, managing expenses, and making informed purchasing decisions.
