How much water must be added to 10 quarts of an 8% concentrated detergent to reduce the concentration to 5%?

Question

what are the steps to solving this equation?

Answer 1

You have 10 quarts of an 8% concentration of detergent. That means that 8% of the solution is detergent. So you have 0.08·10=0.8 quarts of detergent.

 

So if we have 0.8 quarts of detergent, how much water must there be for 0.8 to be 5% of the solution? If the solution has volume x, then 0.8=0.05x, or 80=5x, or 16=x.

 

So to get to the desired concentration, we must end up with 16 quarts of solution. We already have 10 quarts, so we need to add 16-10=6 quarts of water.