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Answer :
To determine the number of songs Miguel can buy, considering the gift card and additional fee, we'll form inequalities based on the given conditions:
1. Understand the Costs:
- Activation fee: [tex]\( \$1.00 \)[/tex]
- Cost per song: [tex]\( \$1.50 \)[/tex]
- Gift card value: [tex]\( \$25 \)[/tex]
2. Set Up the Inequality:
- The total cost for buying [tex]\( m \)[/tex] songs includes the activation fee plus the cost for each song.
- Total cost: [tex]\( 1 + 1.5m \)[/tex]
- This total cost must not exceed Miguel's gift card value, which is [tex]\( \$25 \)[/tex].
3. Write the Inequalities:
- The inequality representing the maximum amount within the gift card is:
[tex]\[
1 + 1.5m \leq 25
\][/tex]
- We can also express this in another form by rewriting it as:
[tex]\[
25 \geq 1 + 1.5m
\][/tex]
4. Inequalities Validity Check:
- Both inequalities represent the same condition, just written differently.
- Based on these expressions, Miguel can purchase songs while ensuring the total cost doesn't exceed the gift card value.
Hence, the two inequalities that represent the situation correctly are:
- [tex]\( 1 + 1.5m \leq 25 \)[/tex]
- [tex]\( 25 \geq 1 + 1.5m \)[/tex]
These options ensure Miguel stays within the limit of his [tex]\( \$25 \)[/tex] gift card after paying the activation fee and purchasing songs.
1. Understand the Costs:
- Activation fee: [tex]\( \$1.00 \)[/tex]
- Cost per song: [tex]\( \$1.50 \)[/tex]
- Gift card value: [tex]\( \$25 \)[/tex]
2. Set Up the Inequality:
- The total cost for buying [tex]\( m \)[/tex] songs includes the activation fee plus the cost for each song.
- Total cost: [tex]\( 1 + 1.5m \)[/tex]
- This total cost must not exceed Miguel's gift card value, which is [tex]\( \$25 \)[/tex].
3. Write the Inequalities:
- The inequality representing the maximum amount within the gift card is:
[tex]\[
1 + 1.5m \leq 25
\][/tex]
- We can also express this in another form by rewriting it as:
[tex]\[
25 \geq 1 + 1.5m
\][/tex]
4. Inequalities Validity Check:
- Both inequalities represent the same condition, just written differently.
- Based on these expressions, Miguel can purchase songs while ensuring the total cost doesn't exceed the gift card value.
Hence, the two inequalities that represent the situation correctly are:
- [tex]\( 1 + 1.5m \leq 25 \)[/tex]
- [tex]\( 25 \geq 1 + 1.5m \)[/tex]
These options ensure Miguel stays within the limit of his [tex]\( \$25 \)[/tex] gift card after paying the activation fee and purchasing songs.
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