Mixing ingredients where portion of one of ingredients is a fn of the final amount
I have two mixtures of flour and water.
Mixture 1 has equal parts flour and water
Mixture 2 has two parts flour to one part water
I also have supplies of flour and water
Problem (a) I'm going to mix flour and water and want to end up with mixture 1 -- equal parts flour and water. BUT in doing so I have to include an amount of Mixture 2 that is 1/6 of the total amount of mixture I end up with (i.e., 1/6 of the total of flour, water, and mixture 2).
Problem (b) is similar -- I'm going to mix flour and water and want to end up with mixture 2 -- two to one ratio of flour to water. BUT I have to include an amount of Mixture 1 that is 1/7 of the total end result.
This is my first post and not a school/college question(Nod)
At 58 am a bit rusty on this stuff hence the question here.
My initial thoughts
M1 = Mixture 1 = 0.5F +0.5W
M2 = Mixture 2 = 2.0F +1.0W
Ma = Mixture a = 0.5F + 0.5W at the end but must be made up of enough of M2 so as to constitute 1/6th of Ma
Ma = xF + yW + 1/6 (Ma)(M2).....