Pounds of Coins

So here is the deal. I was thinking of bringing my Guinness piggybank to the bank tomorrow. Where the bank will use an automated machine to count the change. I wondered if there was some way I could estimate how much money was in it, without actually counting all of it. I figured maybe weight would work, hoping that the distribution of coins would be the same in different sample sizes, giving me a linear relationship. Obviously more coins would have to be worth more, is a pound of pennies worth more than a pound of quarters.. hmm.. good next experiment.
I digress. Three samples 24.9 oz, 14.7 oz, and 7.8 oz. Valuing at 21.31, 12.78, and 7.06 respectively. I plotted these out, amazingly you get a linear relationship. So I predict that since my fully piggy bank weighs 151.5 oz, I should have about $126 in it. I"ll find out tomorrow.