Problem An order is placed with a plant to deliver 2500 kg o

Problem:

An order is placed with a plant to deliver 2500 kg of a 9.5% solution of cellulose nitrate. The only product on hand is a 5.5% solution. How much dry cellulose nitrate must be added to the solution to meet the requirement?

The solution is 106 lbs of dry cellulose nitrate. However, I would like to see all the steps in order to see how the answer was obtained.

Thank you in advance.

Solution

The answer is as follows

let x = mass of pure cellulose nitrate to be added

Now from cellulose nitrate balance:

(2500 kg)(0.095) = (x)(1.0) + (2500 kg - x)(0.055)

Thus x = 105.82 kg. of pure cellulose nitrate

It means you have to combine 105.82 kg. of pure cellulose nitrate to 2,394.18 kg. of the 5.5% cellulose nitrate solution.