An adhesive dealer receives an order for 3000 lb of an adhesive solution containing 13% polymer by weight. On hand are 500 lb of 10% solution and very large quantities of 20% solution and pure solvent. Calculate the weight of each that must be blended together to fill this order. Use all of the 10% solution.

500 lb of 10% solution 1700 lb of 20% solution 800 lb of pure solvent

Explanation:

The mass of polymer in the order recieved is:

3000 lb * 13/100 = 390 lb

The mass of polymer in the 10% solution is:

500 lb * 10/100 = 50 lb

So to solve this problem, we need to add (390-50) 340 lb of polymer that comes from the 20% solution.

We calculate the mass of the 20% solution that would contain 340 lb of polymer:

340 lb * 100/20 = 1700 lb

So far, in total we have a solution that weighs (1700+500) 2200 lb and contains 390 lb of polymer.

Thus, in order to reach the required mass of solution (and percentage of polymer by weight), we add (3000-2200) 800 lb of pure solvent.