need to figure out how much of the 10% bleach needs to be added to the 25% bleach

Question

Using the appropriate concentration of bleach is essential to keeping whites white. Becky has found two solutions of bleach on her shelf. The first bottle contains half a gallon of 25% bleach. There is another container that has a solution of 10% bleach. How much of the 10% bleach must she add to the first bottle of bleach to obtain a solution with 15% bleach?

Answer 1

Sean, I hope I can still help.  I had to think about this one, but let's do it!

 

Let x = the amount of 10% bleach and y = the amount of 15% bleach.

 

We know then that our final amount is going to be the first two amounts added together.

 

x + .5 = y.

 

For our solutions, we multiply the percent (as a decimal) by the amount.  

 

.10x + .25(.5) = .15y.

 

Now, we have a "value" for y from the first equation that we can substitute for y in the 2nd equation.

 

.10x + .25(.5) = .15(.5 + x)

 

Multiply out, including the distributing.

 

.10x + .125 = .075 + .15x

 

Let's multiply both sides by 1000 to get rid of those pesky decimals!

 

100x + 125 = 75 + 150x

 

Now, combine like terms.

 

-50x = -50

     x = 1

 

This means we need 1 gallon of the 10% bleach.  We don't need to solve for y because it doesn't ask for that, but we'd obviously have 1 1/2 gallons of 15% bleach to work with, since we are adding the 1 gallon to the 1/2 gallon we have.

 

Hope this helps!