Since the cost of each book is $12, and x is the number of books, the total cost of books will be 12x.,
Similarly, since the cost of each DVD is $15, and y is the number of DVDs, the total cost of DVDs will be 15y.
Thus, the total cost of books and DVDs will be 12x + 15y.
We know that the total cost was less than $120, so this expression should be less than 120.
Thus, the inequality is:
[tex]12x+15y<120[/tex]Which corresponds to alternative B.
To check wether the amount in the alternatives can be purchased, we just need to substitute x and y and check wether the inequality is valid:
A
[tex]\begin{gathered} 12\cdot5+15\cdot5<120(?) \\ 60+75<120(?) \\ 135<120\to invalid \end{gathered}[/tex]B
[tex]\begin{gathered} 12\cdot6+15\cdot2<120(?) \\ 72+30<120(?) \\ 102<120\to valid \end{gathered}[/tex]C
[tex]\begin{gathered} 12\cdot2+15\cdot6<120(?) \\ 24+90<120(?) \\ 114<120\to valid \end{gathered}[/tex]D
[tex]\begin{gathered} 12\cdot0+15\cdot10<120(?) \\ 0+150<120(?) \\ 150<120\to invalid \end{gathered}[/tex]E
[tex]\begin{gathered} 12\cdot8+15\cdot0<120(?) \\ 96+0<120(?) \\ 96<120\to valid \end{gathered}[/tex]Thus, the amounts that could have been purchased are thouse in alternatives B, C and E.