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
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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