My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Thanks Tree2Thanks
  • 1 Post By romsek
  • 1 Post By skeeter
Reply
 
LinkBack Thread Tools Display Modes
January 6th, 2017, 08:55 PM   #1
Member
 
Joined: Jan 2017
From: US

Posts: 86
Thanks: 5

Red face 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.
Indigo28 is offline  
 
January 6th, 2017, 10:00 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: CA

Posts: 1,302
Thanks: 666

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

$\begin{pmatrix}1 &1 \\0.04 &0.01 \end{pmatrix}\begin{pmatrix}v_1 \\v_2\end{pmatrix} = \begin{pmatrix}15 \\0.3 \end{pmatrix}$
Thanks from Indigo28
romsek is offline  
January 7th, 2017, 07:22 AM   #3
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,611
Thanks: 1297

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

$x+y=15$

$x(4\text{%}) + y(1\text{%}) = 15(2\text{%})$
Thanks from Indigo28
skeeter is offline  
January 7th, 2017, 04:40 PM   #4
Member
 
Joined: Jan 2017
From: US

Posts: 86
Thanks: 5

Thank you, this was really helpful!!
Indigo28 is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
algebra, equations, find, mixture, problem, system



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
a hard problem involving a system of equations davedave Pre-Calculus 4 June 23rd, 2016 02:33 AM
To find a system of coordinates for visualise a system of equations Jhenrique Geometry 1 August 29th, 2015 06:33 AM
Can you help find this system of equations please badmathdog Algebra 2 September 29th, 2014 03:02 AM
System of equations (practical problem) dapias09 Elementary Math 2 July 26th, 2014 07:11 AM
system of equations (find x,y,z) questions shin777 Algebra 4 November 19th, 2011 11:06 PM





Copyright © 2017 My Math Forum. All rights reserved.