SOLUTION: Hi Bob had some money left after spending $9 on 4 files and 6 pens. If he were to buy one more file, he would be short 30cents. If he were to buy one more pen he would have 70 cen

Let F be the price for each file;  P be the price for each pen, and

let X be the amount of money that Bob had initially.


Then, based on the problem's description, we can write these THREE equations for three unknowns


    4F + 6P = 900     cents     (1)     (he spent $9 on 4F and 6P)

    5F + 6P = X + 30  cents     (2)     (he would be short 30 cents)

    4F + 7P = X - 70  cents     (3)     (he would be 70 cents left)



        The setup is just completed. 
        As I said at the beginning, it is tricky.
        But the solution of equations is simple.



To solve them, first subtract equation (3) from equation ((2).  You will get

    F - P   =     100  cents.   (4)


Next, express  F = P + 100 from (4), and substitute it into equation (1).  You will get

    4(P + 100) + 6P = 900

        10P         = 900 - 400 = 500

          P                     = 500/10 = 50.


Next, from equation (1),  4F + 6*50 = 900,  4F = 900 - 300 = 600,  F = 600/4 = 150.


Thus, the price for one file is $1.50;  the price for one pen is  P = F - 100 = 150-100 = 50 = $0.5  (from equation (4))

and  X = 5F + 6P - 30 = 5*150 + 6*50 - 30 = 1020 cents = $10.20.  (from equation (2) )


ANSWER.  The price for each file is  $1.50.  Bob had  $10.20  originally.