A box holding only pennies, dimes, and nickels contains 47 coins worth $3.53. How many of each type of coin are in the box?
The Attempt at a Solution
Ok. So from the problem I can generate two equations:
Were I given three equations, I could easily solve this using an augmented matrix. But, I only have two equations so I can't. Our linear instructor said that we would have to draw some conclusions from the information in order to solve the problem, yet we must show that we didn't do it simply by trial and error.
So the conclusions I have drawn thus far are:
#of pennies (x1) can only be 3, 8, 13, 18, 23, 28, 33, 38, 43
#of dimes (x2) can only be <=35
#of nickels (x3) can only be <=47
(these are the absolute bounds of those numbers, and I realize that 47 nickels is obviously incorrect but for informations sake I wrote it that way)
Also obviously one penny, one dime, and one nickel add up to $0.16 but I can't make an equation out of this
It seems to me that there are *possibly* several solutions to this problem. I have already found one, but I can't just write it down and circle it as I need to show how I found it without using trial and error.
Is there some way to generate a third equation from simple logic? I guess I just want some input on how to attack this.