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Answer :
Let's break down the problem and solve it step by step.
We know that:
- Miguel has a gift card worth [tex]$25.
- Each song costs $[/tex]1.50.
- There is a one-time account activation fee of [tex]$1.00.
We need to find how many songs, represented by \( m \), Miguel can buy without exceeding his gift card value.
Let's create an inequality to reflect this situation:
1. Calculate Total Cost:
The total cost is the sum of the account activation fee and the cost of the songs.
\[
\text{Total Cost} = 1.00 + 1.50 \times m
\]
2. Set the Inequality:
This total cost should be less than or equal to the total value of the gift card, which is $[/tex]25.
[tex]\[
1 + 1.5m \leq 25
\][/tex]
This represents the first inequality option where the total cost does not exceed the gift card value.
3. Find Another Inequality Form:
We can also express it as the total cost being strictly less than the gift card value:
[tex]\[
1 + 1.5m < 25
\][/tex]
Thus, Miguel's spending should satisfy either of these two inequalities:
- [tex]\( 1 + 1.5m \leq 25 \)[/tex]
- [tex]\( 1 + 1.5m < 25 \)[/tex]
Based on the options given, the correct choices are:
- [tex]\( 1 + 1.5m \leq 25 \)[/tex]
- [tex]\( 1 + 1.5m < 25 \)[/tex]
These two inequalities ensure that Miguel's total expenditure will stay within the limit of the gift card.
We know that:
- Miguel has a gift card worth [tex]$25.
- Each song costs $[/tex]1.50.
- There is a one-time account activation fee of [tex]$1.00.
We need to find how many songs, represented by \( m \), Miguel can buy without exceeding his gift card value.
Let's create an inequality to reflect this situation:
1. Calculate Total Cost:
The total cost is the sum of the account activation fee and the cost of the songs.
\[
\text{Total Cost} = 1.00 + 1.50 \times m
\]
2. Set the Inequality:
This total cost should be less than or equal to the total value of the gift card, which is $[/tex]25.
[tex]\[
1 + 1.5m \leq 25
\][/tex]
This represents the first inequality option where the total cost does not exceed the gift card value.
3. Find Another Inequality Form:
We can also express it as the total cost being strictly less than the gift card value:
[tex]\[
1 + 1.5m < 25
\][/tex]
Thus, Miguel's spending should satisfy either of these two inequalities:
- [tex]\( 1 + 1.5m \leq 25 \)[/tex]
- [tex]\( 1 + 1.5m < 25 \)[/tex]
Based on the options given, the correct choices are:
- [tex]\( 1 + 1.5m \leq 25 \)[/tex]
- [tex]\( 1 + 1.5m < 25 \)[/tex]
These two inequalities ensure that Miguel's total expenditure will stay within the limit of the gift card.
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