Welcome to the article You know that 4 notebooks and 3 pens cost 96 while 2 pens and 2 notebooks cost 54 How many dollars are 8 notebooks and. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
Answer:
Let p be the number of pens and let n be the number of notebooks.
4 notebooks + 3 pens cost $96 so 4n + 3p = 96
2 notebooks + 2 pens cost $54 so 2n + 2p = 54
We find n and p by solving the system of linear equations:
4n + 3p = 96
2n + 2p = 54
4n + 3p = 96
4n + 4p = 108 (we multiply this by 2 to cancel out 4n in both equations)
We then subtract the two equations:
(4n + 3p) - (4n + 4p) = 96 - 108
-p = -12
p = 12
So, a pen costs 12 dollars. We can use p to find n. We substitute 12 for p in one of our earlier equations:
2n + 2p = 54
2n + 2(12) = 54
2n + 24 = 54
2n = 30
n = 15
So, a notebook costs 15 dollars and a pen costs 12. Now, we need to find the cost of 8 notebooks and 7 pens:
8n + 7p = ?
8(15) + 7(12) = ?
120 + 84 = 204.
Thus, 8 notebooks and 7 pens cost 204 dollars (why is it so expensive lol).
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Rewritten by : Brahmana