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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

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 Situa class=

Sagot :

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.

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