Derive a general expression for the dilution of saltwater

[mckaybreuner]

Homework Statement

A seashore sand mixture contains 85% insoluble sand, 12% salt, and 3% water by weight. 100 kilograms of this mixture is to be washed by batch operations so that it will contain less than 0.2% salt after drying. In each washing, the sand mixture is mixed with 200 kilograms of water and the resulting saline solution is discarded. The sand mixture retains 0.5 kilograms of water per kilogram of insoluble sand after each washing. Derive a general expression for the weight fraction of salt in the dried mixture after N washings.

Relevant Equations

"N-1" is an exponent in the general expression they are after.

I know that it will take 3 washings to reach the desired purity of sand, and that "N-1" is an exponent in the general expression, but I am stuck beyond that.

 

[Charles Link]

I could not follow the problem statement. It doesn't seem to give any info on how much salt remains after each wash.

 

[mjc123]

I assume the salt is completely soluble, and how much salt remains is determined by how much (salty) water is retained.

 

[mckaybreuner]

@mjc is correct. Thanks for the back and forth I figured it out though: 2.51 x (42.5/242/5)^n-1