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January 6th, 2017, 08:55 PM  #1 
Senior Member Joined: Jan 2017 From: US Posts: 120 Thanks: 6  How Would You Find a System of Equations from this Algebra Mixture Problem?
So, I was given this algebra problem: How many gallons of milk containing 4% fat must be mixed with milk containing 1% fat to obtain a 15 gallon mixture containing 2% fat? And I have to create a system of equations for this problem, and define variables. I am going to be really honest, I really have no idea where to start with this. I had this same problem a while back, and had to find the answer (which is 5 gallons of 4% and 10 gallons of 1%). However, I did not need to make equations with variables to find the answer. If anyone could point me in the right direction it would be very much appreciated! Thanks! Last edited by Indigo28; January 6th, 2017 at 09:06 PM. 
January 6th, 2017, 10:00 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,588 Thanks: 1432 
you have 3 buckets 1 contains some amount of 4% fat milk 1 contains some amount of 1% fat milk the 3rd starts out empty You fill the 3rd bucket with $v_1$ from the first bucket and $v_2$ from the second subject to the following two conditions. $v_1 + v_2 = 15$ $(0.04)v_1 + (0.01)v_2 = 15(0.02) = 0.3$ your equations in matrix form become $\begin{pmatrix}1 &1 \\0.04 &0.01 \end{pmatrix}\begin{pmatrix}v_1 \\v_2\end{pmatrix} = \begin{pmatrix}15 \\0.3 \end{pmatrix}$ 
January 7th, 2017, 07:22 AM  #3  
Math Team Joined: Jul 2011 From: Texas Posts: 3,034 Thanks: 1621  Quote:
$y$ = number of gallons of 1% fat $x+y=15$ $x(4\text{%}) + y(1\text{%}) = 15(2\text{%})$  
January 7th, 2017, 04:40 PM  #4 
Senior Member Joined: Jan 2017 From: US Posts: 120 Thanks: 6 
Thank you, this was really helpful!! 

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algebra, equations, find, mixture, problem, system 
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