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Answer :
To solve this question, we need to determine the inequalities that correctly represent the situation where Miguel uses his [tex]$25 gift card to buy songs, considering the costs involved.
Here's how we approach this problem:
1. Understand the Costs:
- Each song costs $[/tex]1.50.
- There is an activation fee of [tex]$1.00 which applies once regardless of the number of songs bought.
2. Define the Budget:
- Miguel has $[/tex]25 on his gift card.
3. Setting Up the Inequality:
- The total cost to purchase songs can be expressed as the sum of the activation fee and the cost of the songs. This is represented by the expression: [tex]\( 1 + 1.5m \)[/tex], where [tex]\( m \)[/tex] is the number of songs Miguel buys.
- The total cost must be less than or equal to the amount on the gift card. Therefore, one possible inequality is:
[tex]\[
1 + 1.5m \leq 25
\][/tex]
4. Alternate Representation:
- Another way to express this situation is to ensure that the gift card amount is greater than the total cost. This gives us:
[tex]\[
25 > 1 + 1.5m
\][/tex]
Now, let's match these findings with the options provided:
- The inequality [tex]\( 1 + 1.5m \leq 25 \)[/tex] matches the first option.
- The inequality [tex]\( 25 > 1 + 1.5m \)[/tex] matches the third option.
Therefore, the two correct inequalities that represent the situation are:
- [tex]\( 1 + 1.5m \leq 25 \)[/tex]
- [tex]\( 25 > 1 + 1.5m \)[/tex]
Here's how we approach this problem:
1. Understand the Costs:
- Each song costs $[/tex]1.50.
- There is an activation fee of [tex]$1.00 which applies once regardless of the number of songs bought.
2. Define the Budget:
- Miguel has $[/tex]25 on his gift card.
3. Setting Up the Inequality:
- The total cost to purchase songs can be expressed as the sum of the activation fee and the cost of the songs. This is represented by the expression: [tex]\( 1 + 1.5m \)[/tex], where [tex]\( m \)[/tex] is the number of songs Miguel buys.
- The total cost must be less than or equal to the amount on the gift card. Therefore, one possible inequality is:
[tex]\[
1 + 1.5m \leq 25
\][/tex]
4. Alternate Representation:
- Another way to express this situation is to ensure that the gift card amount is greater than the total cost. This gives us:
[tex]\[
25 > 1 + 1.5m
\][/tex]
Now, let's match these findings with the options provided:
- The inequality [tex]\( 1 + 1.5m \leq 25 \)[/tex] matches the first option.
- The inequality [tex]\( 25 > 1 + 1.5m \)[/tex] matches the third option.
Therefore, the two correct inequalities that represent the situation are:
- [tex]\( 1 + 1.5m \leq 25 \)[/tex]
- [tex]\( 25 > 1 + 1.5m \)[/tex]
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