Write a linear inequality that represents this situation. Let x represent the n

label Mathematics
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You have $45 to spend at the music store. Each cassette tape costs $5 and each CD costs $12. Write  a linear inequality that represents this situation. Let x represent the number of tapes and y the number of CDs.

a.  12 x +  5 y   ≥ 45
b.  5 x + 12 y ≤  45
c.  12 x + 5 y ≤  45
d.  5 x + 12 y  ≥  45
Apr 29th, 2015

You have a MAXIMUM of $45 dollars to spend.  Therefore, the total money you spend on CDs PLUS on cassette tapes cannot exceed $45 dollars.  In other words, the total cost of CDs PLUS cassette tapes must be LESS THAN OR EQUAL to the money you have to spend which is $45 dollars.  So, translating that to an inequality looks like:

[cost of CDs] + [cost of cassettes] <= $45

Now, we need to write a mathematical expression for the [cost of CDs] and for [cost of cassettes].  First consider the cost of CDs.  We know that each CD costs $12 (given in the problem).  It also says that "y" represents the number of CDs (given).  So, if we bought "y" amount of CDs, and each one cost $12, then the TOTAL amount we spent on CDs must be $12 multiplied by "y".  Or, we will say we spend 12y.

So, [cost of CDs] can be replaced with 12y.

Similarly with the total cost of cassettes, we know each cassette costs $5 (given in the problem), and "x" represents how many cassettes we bought (given).  So, the total amount we spend buying those cassettes is $5 multiplied by "x", or 5x.

[cost of cassettes] can be replaced with 5x.

Now rewriting the inequality above:

[cost of CDs] + [cost of cassettes] <= 45  becomes....

12y + 5x <= 45

So the answer is B.

Apr 29th, 2015

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