Question 1103791: A number of quarts of apple juice worth .35 cents per quart and a number of quarts of orange juice worth .15 cents per quart is to be mixed to produce 100 gal. of fruit juice for sale at .80 cents per gal. Calculate amts. of apple and orange juice used.
Let x = amt. of apple juice.
Let y = amt. of orange juice.
4 quarts = 1 gal.
Not sure how to solve. Non-homework.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! 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
Second equation,
Revise System:
If using or starting with Elimination Method, multiply the "x+y" equation by 3.
 ------gallons of apple juice
therefore
 ------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
(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:
 , ,     ;
Clear the decimals in the second equation by multiplication of left and right members by 20,...
 *
 -------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?
Answer by ikleyn(52781)  (Show Source):
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