Answer:
Part A: [tex]12x+15y<120[/tex]
Part B: B,C, and E
Step-by-step explanation:
Part A:
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.
Part B:
To check whether the amount in the alternatives can be purchased, we just need to substitute x and y and check whether the inequality is valid:
I'm going to work out these equations :)
Option A.
[tex]12~x~5+15~x~5<120(?)[/tex]
[tex]60+75<120(?)[/tex]
[tex]135<120-->~invalid[/tex]
Option B
[tex]12~x~6+15~x~2<120(?)[/tex]
[tex]102<120--> ~valid[/tex]
Option C.
[tex]12~x~2+15~x~6<120(?)[/tex]
[tex]114<120(?)-->~valid[/tex]
Option D.
[tex]12~x~0+15~x~10<120(?)[/tex]
[tex]0+150<120(?)[/tex]
[tex]150<120-->~invalid[/tex]
Option E
[tex]12~x~8+15~x~0<120(?)[/tex]
[tex]96+0<120(?)[/tex]
[tex]96<120--->~Valid[/tex]
Thus, the amounts that could have been purchased are those in alternatives B, C and E.
