Question 1103791
Mixture problem in which concentration is MONEY per VOLUME

Do all as dollars and gallons; assuming you meant "dollars" instead of "cents";


APPLE JUICE,  0.35*4=1.4  dollars per gallon
ORANGE JUICE, 0.15*4=0.6 dollars per gallon


x gallons Apple juice
y gallons Orange juice


{{{system(x+y=100,1.4x+0.6y=(0.8)(100))}}}


Second equation,
{{{14x+6y=800}}}
{{{7x+3y=400}}}


Revise System:
{{{system(7x+3y=400,x+y=100)}}}


If using or starting with Elimination Method, multiply the "x+y" equation by 3.

{{{system(7x+3y=400,3x+3y=300)}}}


{{{(7x+3y)-(3x+3y)=400-300}}}

{{{4x=100}}}

{{{highlight(x=25)}}}------gallons of apple juice
therefore
{{{highlight(y=75)}}}------gallons of orange juice








THIS BELOW IS A LITTLE LESS EFFICIENT (and mixed up x and y)
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If you want x for amount apple juice and y for amount orange juice, and 100 gallons of mixture to be 0.80 dollars per gallon


{{{system(x+y=100,(0.15x+0.35y)*4=0.8*100)}}}
(I assumed you meant to say, 0.35 dollars per quart and 0.15 dollars per quart; instead of "cents").


The multiplication by 4 on left member of the second equation is to change from quarts to gallons.  You can work the solution all in dollars and gallons.  Convert to quarts later if you want.


Starting with that second equation:
{{{4(0.15x+0.35y)=(0.80)(100)}}}
{{{0.15x+0.35y=(0.80)(100)/4}}}, , {{{just}}}{{{do_the}}}{{{arithmetic}}}{{{on_the_right}}};
{{{0.15x+0.35y=20}}}



{{{system(x+y=100,0.15x+0.35y=20)}}}

Clear the decimals in the second equation by multiplication of left and right members by 20,...
{{{system(3x+7y=400,x=100-y)}}}    *


{{{3(100-y)+7y=400}}}-------substituted for x, giving one equation in just one variable y, simplify this and solve.  Use the result to find x.




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* Did you still want help on this part?
{{{0.15x+0.35y=20}}}
{{{100(0.15x+0.35y)=100*20}}}
{{{15x+35y=100*20}}}
{{{(1/5)(15x+35y)=(1/5)(100)(20)}}}

{{{3x+7y=20*20}}}

{{{3x+7y=400}}}