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Can someone please help me?

Can someone please help me?-example-1

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Answer:

Part A:
12x+15y<120

Part B: B,C, and E

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:


12x+15y<120

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.


12~x~5+15~x~5<120(?)


60+75<120(?)


135<120-->~invalid

Option B


12~x~6+15~x~2<120(?)


102<120--> ~valid

Option C.


12~x~2+15~x~6<120(?)


114<120(?)-->~valid

Option D.


12~x~0+15~x~10<120(?)


0+150<120(?)


150<120-->~invalid

Option E


12~x~8+15~x~0<120(?)


96+0<120(?)


96<120--->~Valid

Thus, the amounts that could have been purchased are those in alternatives B, C and E.

User Catherine Hwang
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