Dishwashing mathmatical help needed!
Hey, I'm new here, because I dont no where else to go with my bemusing problem...
I'm taking part in a Science Technology Engineering and Mathmatics course, but this problem which I came across is something I haven't covered within my skillset yet...
Firstly, the basic problem is about Re-usable cups vs Disposable cups, but I'm having problems doing a certian energy calculation.
I worked out that the energy cost for a re-usable cup would be:
n/x + x(r) with x being number of uses/washes, r being the energy to wash a cup in a dishwasher in joules (total dishwasher energy/total number of cups) and n being the production energy, also in joules. However, I know some of these values, making the problem:
6,300,000/x + x(64,800) = the total energy (which I will call T)
Now what I got stuck on is this...
I know it takes 310,000 joules of energy to make a plastic disposable cup. I want to find out how many times I need to use and wash the cup to get a payback time on my re-using.
So I got T=6,300,000/x + x(64,800)
But with T being 310,000
310,000 = 6,300,000/x + 64800x
But how do I find x?
I end up with:
6,300,000/x + x(64,800) = 310,000
6,300,000/x + 64,800x = 310,000
64,800x + 6,300,000/x = 310,000
64,800x = 310,000 - 6,300,000/x
and I just stop...
Have I gone wrong somewhere?