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-   -   How Would You Find a System of Equations from this Algebra Mixture Problem? (http://mymathforum.com/algebra/338434-how-would-you-find-system-equations-algebra-mixture-problem.html)

 Indigo28 January 6th, 2017 09:55 PM

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!

 romsek January 6th, 2017 11:00 PM

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

$\begin{pmatrix}1 &1 \\0.04 &0.01 \end{pmatrix}\begin{pmatrix}v_1 \\v_2\end{pmatrix} = \begin{pmatrix}15 \\0.3 \end{pmatrix}$

 skeeter January 7th, 2017 08:22 AM

Quote:
 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?
let $x$ = number of gallons of 4% fat

$y$ = number of gallons of 1% fat

$x+y=15$

$x(4\text{%}) + y(1\text{%}) = 15(2\text{%})$

 Indigo28 January 7th, 2017 05:40 PM

Thank you, this was really helpful!! :)

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