High School

Miguel can use all or part of his [tex]\$25[/tex] gift card to make a music purchase. Each song costs [tex]\$1.50[/tex], and there is a [tex]\$1.00[/tex] account activation fee.

Which inequalities can represent this situation if [tex]m[/tex] is the number of songs he can buy? Select two options.

A. [tex]1 + 1.5m \leq 25[/tex]

B. [tex]1 + 1.5m \geq 25[/tex]

C. [tex]25 > 1 + 1.5m[/tex]

D. [tex]1 + 1.5m < 25[/tex]

E. [tex]25 \geq 1 + 1.5m[/tex]

Answer :

Let's denote the number of songs Miguel buys by [tex]$m$[/tex]. Each song costs \[tex]$1.50, and there is a \$[/tex]1 account activation fee. Thus, the total cost for [tex]$m$[/tex] songs is given by

[tex]$$
\text{Total Cost} = 1 + 1.5m.
$$[/tex]

Miguel's gift card is worth \[tex]$25, so the total cost must be at most \$[/tex]25. This requirement can be written as

[tex]$$
1 + 1.5m \leq 25.
$$[/tex]

This inequality is equivalent to writing

[tex]$$
25 \geq 1 + 1.5m.
$$[/tex]

Hence, the two valid representations of the situation are:

1. [tex]$$1 + 1.5m \leq 25,$$[/tex]
2. [tex]$$25 \geq 1 + 1.5m.$$[/tex]

These correspond to the options marked as Option 1 and Option 5.

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