College

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] per 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 \ \textgreater \ 1 + 1.5m[/tex]

D. [tex]1 + 1.5m \ \textless \ 25[/tex]

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

Answer :

First, note that Miguel has a \[tex]$25 gift card. When he makes a music purchase, there is an account activation fee of \$[/tex]1.00, and each song costs \[tex]$1.50. If he buys $[/tex]m[tex]$ songs, then his total cost is given by

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

Since his total cost cannot exceed \$[/tex]25, we set up the inequality

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

This inequality also can be written as

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

Therefore, the two inequalities that represent the situation are

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

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