Question 794741
Assumption:  The water is the second part, and your component material is the first part, so giving ratios as  Component:Water.


Your calculations should be easier converted into ordinary fractions. 


Your ratios give:
{{{1/(1+4)}}} component solution, available
and
{{{1/(1+6)}}} component solution, wanted


Those are 
{{{1/5}}} component available
and 
{{{1/7}}} component wanted


You want to add v fluid ounces of water which will not change the AMOUNT of Component; it will  only change the CONCENTRATION of component.


See carefully, you have 4 MILILITERS of available (1/5) concentration solution but you want to add v FLUID OUNCES of water.  I will setup the equations assuming mililiters.  You can find and use the conversion factor for these two units on your own.


{{{highlight((4(1/5))/(4+v)=(1/7))}}}
Again as I said, after solving for v, you need to convert from mililiters to fluid ounces  ( NOT "ounces").