Thread: 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


At 58 am a bit rusty on this stuff hence the question here.


My initial thoughts


F= flour
W= water
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).....
Thanks

The equation you wrote looks sensible, but you need more than 1 equation to solve the problem.

If you define:

F = the amount of flour you added
W = the amount of water you added
M2 = the amount of mixture 2 added

The total amount of water in your output is


And the total amount of Flour is


To end up with mixture1, you need to have the same amount of flour and water


You are also told to use M2 for 1/6 of your input, which means there should be 5 units of standalone (flour + water) for each 1 units of M2.


Now all you need to do is decide how much mixture to make, to do this set an arbitrary amount of one of the ingredients eg


Then solve the other two equations simultaneously.




Which has a solution of
W=7/3
F = 8/3
M2 = 1

NB post was edited to fix a mistake earlier