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).
