Question

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 7 pens worth?

Answer 1

204

Explanation:

:)

Answer 2

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).