Question

Person A went to the store and bought some books at $12 each and some DVDs at $15 each. The bill (before tax) was less than $120. Which inequality represents the situation if x=books and y=DVDs?A) 12x+15y = 120B) 12x+15y < 120C) 12x+15y >-D) none of the above

Answer 1

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.

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

`\begin{gathered} 12\cdot5+15\cdot5<120(?) \\ 60+75<120(?) \\ 135<120\to invalid \end{gathered}`

B

`\begin{gathered} 12\cdot6+15\cdot2<120(?) \\ 72+30<120(?) \\ 102<120\to valid \end{gathered}`

C

`\begin{gathered} 12\cdot2+15\cdot6<120(?) \\ 24+90<120(?) \\ 114<120\to valid \end{gathered}`

D

`\begin{gathered} 12\cdot0+15\cdot10<120(?) \\ 0+150<120(?) \\ 150<120\to invalid \end{gathered}`

E

`\begin{gathered} 12\cdot8+15\cdot0<120(?) \\ 96+0<120(?) \\ 96<120\to valid \end{gathered}`

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