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3 votes
3 votes
I really need help and this answered ASAP. thank you and sorry.

At the Cardinal corner Bookstore, three notebooks and two pens cost $6.50, while eight notebooks and four pens cost $16.00. What is the total cost for one notebook and one pen?​

User Kpeatt
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2 Answers

11 votes
11 votes
Answer:
$2.50
I hope this helps!
User Onuriltan
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3.3k points
23 votes
23 votes

9514 1404 393

Answer:

$2.50

Explanation:

The question asks for the total cost of a notebook and pen together. We don't need to find their individual costs in order to answer the question.

Sometimes we get bored solving systems of equations in the usual ways. For this question, let's try this.

The first equation has one more notebook than pens. The second equation has 4 more notebooks than pens. If we subtract 4 times the first equation from the second, we should have equal numbers of notebooks and pens.

(8n +4p) -4(3n +2p) = (16.00) -4(6.50)

-4n -4p = -10.00 . . . . . . . . . . . simplify

n + p = -10.00/-4 = 2.50 . . . . divide by the coefficient of (n+p)

The total cost for one notebook and one pen is $2.50.

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Additional comment

The first equation has 1 more notebook than 2 (n+p) combinations, telling us that a notebook costs $6.50 -2(2.50) = $1.50. Then the pen is $2.50 -1.50 = $1.00.

One could solve for the costs of a notebook (n) and a pen (p) individually, then add them together to answer the question. We judge that to be more work.

User Fast Tooth
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2.7k points