Answer :
Sure! Let's work through the problem step-by-step to find the correct inequalities representing the situation.
Miguel has a [tex]$25 gift card, and he wants to use it to buy songs, each costing $[/tex]1.50. There's also a [tex]$1.00 account activation fee. Let $[/tex]m[tex]$ be the number of songs Miguel can buy.
Step 1: Determine the Total Cost Equation
The total cost for Miguel buying $[/tex]m[tex]$ songs will include both the cost of the songs and the activation fee.
- Activation fee: $[/tex]1.00
- Cost of [tex]$m$[/tex] songs: [tex]$1.50 \times m$[/tex]
Therefore, the total cost [tex]$C$[/tex] can be written as:
[tex]\[ C = 1.00 + 1.50 \times m \][/tex]
Step 2: Set Up the Inequality
Since Miguel cannot spend more than the [tex]$25 on his gift card, the total cost must be less than or equal to $[/tex]25. Therefore, we set up the following inequality:
[tex]\[ 1 + 1.5m \leq 25 \][/tex]
This inequality means that the sum of the account activation fee and the total song cost should not exceed the [tex]$25 gift card balance.
Step 3: Understand the Equivalent Form
The above inequality can also be written with the sides flipped:
\[ 25 \geq 1 + 1.5m \]
This means the same thing: the total money on the gift card ($[/tex]25) is greater than or equal to the total cost of the songs and activation fee.
Conclusion: Identify the Correct Options
Based on the steps above, the two inequalities that describe the situation correctly are:
1. [tex]\( 1 + 1.5m \leq 25 \)[/tex]
2. [tex]\( 25 \geq 1 + 1.5m \)[/tex]
These inequalities ensure that the cost of buying [tex]$m$[/tex] songs plus the activation fee does not exceed [tex]$25.
Therefore, the correct selections are:
- $[/tex]1+1.5 m \leq 25[tex]$
- $[/tex]25 \geq 1+1.5 m$
Miguel has a [tex]$25 gift card, and he wants to use it to buy songs, each costing $[/tex]1.50. There's also a [tex]$1.00 account activation fee. Let $[/tex]m[tex]$ be the number of songs Miguel can buy.
Step 1: Determine the Total Cost Equation
The total cost for Miguel buying $[/tex]m[tex]$ songs will include both the cost of the songs and the activation fee.
- Activation fee: $[/tex]1.00
- Cost of [tex]$m$[/tex] songs: [tex]$1.50 \times m$[/tex]
Therefore, the total cost [tex]$C$[/tex] can be written as:
[tex]\[ C = 1.00 + 1.50 \times m \][/tex]
Step 2: Set Up the Inequality
Since Miguel cannot spend more than the [tex]$25 on his gift card, the total cost must be less than or equal to $[/tex]25. Therefore, we set up the following inequality:
[tex]\[ 1 + 1.5m \leq 25 \][/tex]
This inequality means that the sum of the account activation fee and the total song cost should not exceed the [tex]$25 gift card balance.
Step 3: Understand the Equivalent Form
The above inequality can also be written with the sides flipped:
\[ 25 \geq 1 + 1.5m \]
This means the same thing: the total money on the gift card ($[/tex]25) is greater than or equal to the total cost of the songs and activation fee.
Conclusion: Identify the Correct Options
Based on the steps above, the two inequalities that describe the situation correctly are:
1. [tex]\( 1 + 1.5m \leq 25 \)[/tex]
2. [tex]\( 25 \geq 1 + 1.5m \)[/tex]
These inequalities ensure that the cost of buying [tex]$m$[/tex] songs plus the activation fee does not exceed [tex]$25.
Therefore, the correct selections are:
- $[/tex]1+1.5 m \leq 25[tex]$
- $[/tex]25 \geq 1+1.5 m$
