Question 982911
TYPE__________PERCENT-CONC_______VARIABLE
Low____________25_________________x
Medium_________40_________________y
High___________80_________________z
-
DESCRIPTION:  {{{z/y=3}}}
WANT:  66 liters of 55%


Accounting for volumes
{{{x+y+z=66}}}
{{{x+y+3y=66}}}
{{{x+4y=66}}}


Account for concentrations keeping all as percents
{{{(25x+40y+80z)/(66)=55}}}


z can be eliminated from this, just as done in volume account.
{{{(25x+40y+80*3y)/66=55}}}
Divide members by 5.
{{{(5x+9y+16*3y)/66=11}}}
{{{highlight_green((5x+57y)/66=11)}}}
{{{5x+57y=726}}}


A system of two equations in just x and y is possible.
{{{system(highlight(x+4y=66),highlight(5x+57y=726))}}}


Solve for x and y any way you want or know.


Equivalent:
{{{system(5x+20y=330,5x+57y=726)}}}
subtract first equation from second equation to find y.
{{{highlight(y=10.702*liters)}}}-------the 40% material


Before even finding x,  finding z is possible right now.
{{{z=3*y}}}
{{{z=3*10.702}}}
{{{highlight(z=32.108*liters)}}}------the 80% material


The original volume sum equation most easily will give x.