Question

Craig bought 8 folders and notebooks forschool. Folders cost $0.50 and notebooks cost$1.50. Craig spent a total of $6. How manyfolders (f) and how many notebooks (n) did hebuy?f+ n = 80.5f + 1.5n = 6

Answer 1

We have a sysyem of equations that represent the information we have.

As we have 8 items between the notebooks and folders, we can write:

$f+n=8$

being f: number of folders, and n: number of notebooks.

Then, as each folder costs $0.50 , the notebooks cost $1.50 each and the total cost was $6 we can write:

$0.50f+1.50n=6$

We can solve it by substracting 2 times the second equation from the first. This will create a new linear combination of the two equations that will eliminate f and let us solve for n:

$\begin{gathered} (f+n)-2(0.50f+1.50n)=8-2*6 \\ f+n-2*0.5f-2*1.50n=8-12 \\ f+n-f-3n=-4 \\ 0f-2n=-4 \\ n=\frac{-4}{-2} \\ n=2 \end{gathered}$

We can now use any of the two equations to solve for f. We will use the first one as it is simpler:

$\begin{gathered} f+n=8 \\ f=8-n \\ f=8-2 \\ f=6 \end{gathered}$

We can check with the second equation to verify the solution:

$\begin{gathered} 0.5f+1.5n=6 \\ 0.5*6+1.5*2=6 \\ 3+3=6 \\ 6=6\text{ -->Verified} \end{gathered}$

Answer: 6 folders and 2 notebooks.