SOLUTION: Maggie makes some fruit punch. She mixes 2 1/2 quarts of grape juice with 1 1/2 quarts of orange juice. One quart of grape juice cost $1 less than one quart of orange juice. She fi

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Question 913525: Maggie makes some fruit punch. She mixes 2 1/2 quarts of grape juice with 1 1/2 quarts of orange juice. One quart of grape juice cost $1 less than one quart of orange juice. She finds that the total cost of making the fruit punch is $12.50. Calculate the cost of each quart of grape juice and each quart of orange juice.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Prices Per Quart:
g for grape juice
n for oraNge juice
g=n-1

Account for the cost.
%282%261%2F2%29g%2B%281%261%2F2%29n=12.50
%282%261%2F2%29%28n-1%29%2B%281%261%2F2%29n=12.5
%285%2F2%29%28n-1%29%2B%283%2F2%29n=12.5
5%28n-1%29%2B3n=25
5n-5%2B3n=25
8n=30
n=30%2F8
highighlt%28n=15%2F4%29, $3.75 per quart. Orange Juice.

g for grape juice is $2.75 per quart.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
( quarts ) x ( price / quart ) = total price
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Let +p+ = price/quart of orange juice
+p+-+1+ = price/quart of grape juice
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+1.5p+%2B+2.5%2A%28+p+-+1+%29+=+12.5+
+1.5p+%2B+2.5p+-+2.5+=+12.5+
+4p+=+12.5+%2B+2.5+
+4p+=+15+
+p+=+3.75+
and
+p+-+1+=+2.75+
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The price/quart of orange juice is $3.75
The price/quart of grape juice $2.75
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check:
+1.5p+%2B+2.5%2A%28+p+-+1+%29+=+12.5+
+1.5%2A3.75+%2B+2.5%2A2.75+=+12.5+
+5.625+%2B+6.875+=+12.5+
+12.5+=+12.5+
OK