Question

Can someone please help me?

Answer 1

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.