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Answer :
To solve the problem, we need to establish inequalities that represent the constraints given the gift card, song costs, and the activation fee.
1. Understand the costs involved:
- The gift card value is [tex]$25.
- Each song costs $[/tex]1.50.
- There is a [tex]$1.00 account activation fee.
2. Setup the inequality:
- The total cost includes the activation fee plus the cost of songs Miguel wants to buy. This is given by:
\[
\text{Total cost} = 1 + 1.5m
\]
- Since Miguel can use part or all of his gift card, the total cost must be less than or equal to $[/tex]25. Thus, we get:
[tex]\[
1 + 1.5m \leq 25
\][/tex]
3. Rewrite the inequality:
- We can also express it in reverse:
[tex]\[
25 \geq 1 + 1.5m
\][/tex]
Given these inequalities, look at the options presented:
- Option 1: [tex]\( 1 + 15m \leq 25 \)[/tex]: Incorrect as this is based on a wrong coefficient.
- Option 2: [tex]\( 1 + 1.5m \geq 25 \)[/tex]: Incorrect as it implies that the cost exceeds the gift card value.
- Option 3: [tex]\( 25 > 1 + 1.5m \)[/tex]: Correct, it closely matches the situation.
- Option 4: [tex]\( 1 + 1.5m < 25 \)[/tex]: Correct, as this means the total cost is less than the gift card value.
- Option 5: [tex]\( 25 \geq 1 + 1.5m \)[/tex]: Correct, matches our derived inequality.
Therefore, the correct inequalities to represent this situation are:
- [tex]\( 25 > 1 + 1.5m \)[/tex]
- [tex]\( 25 \geq 1 + 1.5m \)[/tex]
Both of these indicate how many songs Miguel can afford while staying within the balance of his gift card.
1. Understand the costs involved:
- The gift card value is [tex]$25.
- Each song costs $[/tex]1.50.
- There is a [tex]$1.00 account activation fee.
2. Setup the inequality:
- The total cost includes the activation fee plus the cost of songs Miguel wants to buy. This is given by:
\[
\text{Total cost} = 1 + 1.5m
\]
- Since Miguel can use part or all of his gift card, the total cost must be less than or equal to $[/tex]25. Thus, we get:
[tex]\[
1 + 1.5m \leq 25
\][/tex]
3. Rewrite the inequality:
- We can also express it in reverse:
[tex]\[
25 \geq 1 + 1.5m
\][/tex]
Given these inequalities, look at the options presented:
- Option 1: [tex]\( 1 + 15m \leq 25 \)[/tex]: Incorrect as this is based on a wrong coefficient.
- Option 2: [tex]\( 1 + 1.5m \geq 25 \)[/tex]: Incorrect as it implies that the cost exceeds the gift card value.
- Option 3: [tex]\( 25 > 1 + 1.5m \)[/tex]: Correct, it closely matches the situation.
- Option 4: [tex]\( 1 + 1.5m < 25 \)[/tex]: Correct, as this means the total cost is less than the gift card value.
- Option 5: [tex]\( 25 \geq 1 + 1.5m \)[/tex]: Correct, matches our derived inequality.
Therefore, the correct inequalities to represent this situation are:
- [tex]\( 25 > 1 + 1.5m \)[/tex]
- [tex]\( 25 \geq 1 + 1.5m \)[/tex]
Both of these indicate how many songs Miguel can afford while staying within the balance of his gift card.
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