Question

You have $44 to spend at the music store. Each cassette tape costs $10 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.10x + 12y ≤ 44

B.10x + 12y ≥ 44

C.12x + 10y ≥ 44

D.12x + 10y ≤ 44

Answer 1

The answer is A. 10x + 12y ≤ 44

Step-by-step explanation:

A:

The answer is answer choice A because since the number of the cassette tapes is represented by x and the cost of each individual cassette tape is $10, 10 and x would be paired together. And 12 and y would be paired together because the number of CDs is represented by y and the cost of each individual CD is $12. And if you buy two cassette tapes and two CDs, it would add up to exactly $44. So you would put ≤ because 10x + 12y is equal to 44 (if you buy two cassette tapes and two CDs) and it can't be more or you wouldn't be able to buy the items. So that is why the answer is A. 10x + 12y ≤ 44. But first lets review the other answer choices.

B:

The answer isn't answer choice B because even though x and y are paired with the correct numbers, 44 is not less than 10x + 12y.

C:

The answer isn't answer choice C because x wouldn't be paired with 12 because x represents the number of cassete tapes and 12 is how much the CDs cost so it would be paired with y and x would be paired with 10. Again, 44 is not less than the cost of the cassette tapes and CDs.

D:

The answer isn't answer choice D because like I said x is paired with 10 and y is paired with 12. But this choice is correct about 44 not being less than the cost of the cassette tapes and CDs together.

Conclusion:

I hope this answer helps lots of people understand this topic better.

Answer 2

A.10x + 12y ≤ 44

Step-by-step explanation:

Each cassette tape costs $10 and each CD costs $12

Let x represent the number of tapes and y the number of CDs.

The cost of the cassettes is the number of cassettes times the cost per cassette and the cost of the tapes is the number of tapes times the cost per tape. We add these together to get the total cost. The total cost must be less than or equal to 44

44≥10x+12y