Answer:
1.67 gallons
Step-by-step explanation:
Given that:
Original mixture contains 80% detergent and 20% water in a 15 gallon bucket.
New Mixture to contain 60% detergent and 40% water of 5 gallon bucket.
To find:
Volume of Pure water to be added to each 5 gallon bucket to obtain the new mixture.
Solution:
First of all, let us calculate the answer by adding pure water to 15 gallon bucket.
Let the number of gallon of water to be added = [tex]x[/tex]
New volume = (15+[tex]x[/tex]) gallons
Now, let us compare the number of gallons of water in the mixture before and after.
[tex]15\times 20\% + x = (15+x)\times 40\%\\\Rightarrow (3+x)\times 5 = (15+x)\times 2\\\Rightarrow 15+5x=30+2x\\\Rightarrow 3x=15\\\Rightarrow x =5\ gallons[/tex]
Therefore, to a 15 gallon bucket (80% detergent and 20% water)of detergent mixture, if we add 5 gallons of pure water , it will become 60% detergent and 40% water.
To a 5 gallon bucket, the number of gallons of water to be added = [tex]\frac{5}{3} =\bold{1.67\ gallons}[/tex]
