Answer :
To analyze Miguel’s situation, note that he must pay a \$1 activation fee and \$1.50 for each song he buys. Letting \( m \) represent the number of songs, the total cost \( C \) can be written as
$$
C = 1 + 1.50\,m.
$$
Since Miguel has a \$25 gift card, the cost must not exceed \$25, which gives us the inequality
$$
1 + 1.50\,m \leq 25.
$$
To avoid handling decimals, we can multiply the entire inequality by 10. This yields
$$
10 + 15\,m \leq 250,
$$
which, when divided by 10 again (to revert to the original scale), corresponds to the inequality
$$
1 + 15\,m \leq 25.
$$
This inequality is equivalent to
$$
25 \geq 1 + 15\,m.
$$
Thus, the two correct representations of the situation are:
1. \( 1 + 15\,m \leq 25 \)
2. \( 25 \geq 1 + 15\,m \)
These are the two inequalities that accurately represent the condition that the total cost of the songs, including the activation fee, should not exceed \$25.
$$
C = 1 + 1.50\,m.
$$
Since Miguel has a \$25 gift card, the cost must not exceed \$25, which gives us the inequality
$$
1 + 1.50\,m \leq 25.
$$
To avoid handling decimals, we can multiply the entire inequality by 10. This yields
$$
10 + 15\,m \leq 250,
$$
which, when divided by 10 again (to revert to the original scale), corresponds to the inequality
$$
1 + 15\,m \leq 25.
$$
This inequality is equivalent to
$$
25 \geq 1 + 15\,m.
$$
Thus, the two correct representations of the situation are:
1. \( 1 + 15\,m \leq 25 \)
2. \( 25 \geq 1 + 15\,m \)
These are the two inequalities that accurately represent the condition that the total cost of the songs, including the activation fee, should not exceed \$25.
