Question

Manny's cleaning supply store receives a mixture of 80% detergent and 20% water in 15-gallon buckets. Manny would like a mixture of 60 detergent and 40% water in a 5 gallon buckets. To make this he combined some 80/20 mixture with some pure water in each 5 gallon bucket. How much gallons of pure water does Manny add to each 5 gallon bucket.

Answer 1

1.67 gallons

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 =
`x`

New volume = (15+
`x`) gallons

Now, let us compare the number of gallons of water in the mixture before and after.

`15* 20\% + x = (15+x)* 40\%\\\Rightarrow (3+x)* 5 = (15+x)* 2\\\Rightarrow 15+5x=30+2x\\\Rightarrow 3x=15\\\Rightarrow x =5\ gallons`

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 =
`(5)/(3) =\bold{1.67\ gallons}`