Meryl needs to add enough water to 11 gallons of an 18% detergent solution to make a 12% detergent solution. which equation can she use to find g, the number of gallons of water she should add? original added new amount of detergent 1.98 gallons 0 amount of solution 11 gallons g mc008-1.jpg mc008-2.jpg mc008-3.jpg mc008-4.jpg

We're measuring a quantity of pure detergent.  

We start with 11 gallons of an 18% solution.  18% of that, or 1.98 gallons, is pure detergent, and the rest of these 11 gal. is water:  9.02 gal.  We will add x gallons of water to this solution to obtain (11+x) gallons of a 12% solution.

We need to find x to satisfy this equation:

(11 gallons + x)(0.12) = (11 gallons)(0.18)

Div. both sides by 0.12, we get     (11 gallons + x) = (11 gallons)(1.5)

Mult. both sides by 10, we get 110 gallons + 10x = (11 gallons)(15)

Then 10x = 165 gallons - 110 gallons, or 55 gallons.

Div. both sides by 10, we get x = 5.5 gallons (answer)