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Answer :
Certainly! Let's analyze the problem:
Miguel has a [tex]$25 gift card, and he wants to use it to buy songs. Each song costs $[/tex]1.50, and there is also a [tex]$1.00 account activation fee. We want to determine how many songs, represented by \( m \), Miguel can buy without exceeding the $[/tex]25 available on his gift card.
We need to create an inequality to represent this situation:
1. Total Cost Calculation:
- The total cost to buy [tex]\( m \)[/tex] songs can be represented as:
[tex]\[
\text{Total Cost} = \text{activation fee} + (\text{cost of each song} \times m)
\][/tex]
- Plugging in the given values:
[tex]\[
\text{Total Cost} = 1 + 1.50m
\][/tex]
2. Inequality to Respect the Gift Card Limit:
- Since Miguel can't spend more than [tex]$25, the total cost must be less than or equal to the amount on the gift card:
\[
1 + 1.50m \leq 25
\]
3. Alternative Representation of the Situation:
- Another way to express this condition is to ensure the total cost is strictly less than the $[/tex]25, which gives the inequality:
[tex]\[
1 + 1.50m < 25
\][/tex]
Given these calculations, the two inequalities that correctly represent the situation where Miguel can buy songs with his gift card are:
- [tex]\(1 + 1.50m \leq 25\)[/tex]
- [tex]\(1 + 1.50m < 25\)[/tex]
These inequalities show the maximum number of songs Miguel can buy without exceeding the $25 limit on his gift card, given the cost conditions.
Miguel has a [tex]$25 gift card, and he wants to use it to buy songs. Each song costs $[/tex]1.50, and there is also a [tex]$1.00 account activation fee. We want to determine how many songs, represented by \( m \), Miguel can buy without exceeding the $[/tex]25 available on his gift card.
We need to create an inequality to represent this situation:
1. Total Cost Calculation:
- The total cost to buy [tex]\( m \)[/tex] songs can be represented as:
[tex]\[
\text{Total Cost} = \text{activation fee} + (\text{cost of each song} \times m)
\][/tex]
- Plugging in the given values:
[tex]\[
\text{Total Cost} = 1 + 1.50m
\][/tex]
2. Inequality to Respect the Gift Card Limit:
- Since Miguel can't spend more than [tex]$25, the total cost must be less than or equal to the amount on the gift card:
\[
1 + 1.50m \leq 25
\]
3. Alternative Representation of the Situation:
- Another way to express this condition is to ensure the total cost is strictly less than the $[/tex]25, which gives the inequality:
[tex]\[
1 + 1.50m < 25
\][/tex]
Given these calculations, the two inequalities that correctly represent the situation where Miguel can buy songs with his gift card are:
- [tex]\(1 + 1.50m \leq 25\)[/tex]
- [tex]\(1 + 1.50m < 25\)[/tex]
These inequalities show the maximum number of songs Miguel can buy without exceeding the $25 limit on his gift card, given the cost conditions.
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