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 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)
