Question

f $0.30 folders and n $1.50 notebooks total $12

Graph the equation and use the graph to determine three different combinations of folders and notebooks that total $12.

Answer 1

f(.30) + n(1.50) = 12. Looks like we can make a line out of this. make y-axis = n-axis, and x-axis = f-axis.

solve for n I guess:

n = -(1/5)f + 8

any value of "f" will give us a value of "n" that will satisfy the problem. Perferable we want whole number tho.

When f=0, n=8; 8(1.50) = 12.00 is a true statement. Now, for any increment of 5 folders, we will get -1 notebooks.

For example: If we add 5 folders, we should have (8-1) notebooks.

n =-(1/5)(5) + 8 = -1+8 = 7

5(.30) + 7(1.50) ?=? 12.00
1.50 + 10.50 ?=? 12.00

12.00 = 12.00 true.

Now there is a limit, a domain of folders if you will that we cannot stray from. Anything that makes "n" negative has no meaning. It is impossible to sell less than 0 notebooks right? And it makes no sense to sell less than 0 folders.

What makes -(1/5)f + 8 < 0?

8 < (1/5)f

8(5) < f

40 < f

when f > 40, the numbers no longer make any sense.

So lets restrict the domain to [0,40]

The combinations that will make 12.00 will be:

f n
-----
0 8
5 7
10 6
15 5
20 4
25 3
30 2
35 1
40 0

And this concludes our problem :) i think....what am I forgetting?