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 costs $1 less than one quart of orange juice. She f

Algebra ->  Equations -> 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 costs $1 less than one quart of orange juice. She f      Log On


   



Question 922952: 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 costs $1 less than one quart of orange juice. She finds that the total cost of making the fruit punch is $12.50. Caculate the cost of each quart of graph juice And Each quart of orange juice.
PLEASE HELP ME!!!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the cost in CENTS of 1 quart of orange juice
+c+-+100+ = the cost in CENTS of 1 quart of grape juice
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Convert quantities of juice to multiples of +1%2F2+
+%285%2F2%29%2Ac+%2B+%283%2F2%29%2A%28+c+-+100+%29+=+1250+ ( all in CENTS )
Multiply both sides by +2+
+5c+%2B+3%2A%28+c+-+100+%29+=+2500+
+5c+%2B+3c+-+300+=+2500+
+8c+=+2800+
+c+=+350+ cents
+c+-+100+=+250+ cents
1 quart of orange juice cost $3.50
1 quart of grape juice costs $2.50
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check:
+%285%2F2%29%2Ac+%2B+%283%2F2%29%2A%28+c+-+100+%29+=+1250+
+%285%2F2%29%2A350+%2B+%283%2F2%29%2A%28+350+-+100+%29+=+1250+
+%285%2F2%29%2A350+%2B+%283%2F2%29%2A250+=+1250+
Divide both sides by +50+
+35%2F2+%2B+15%2F2+=+25+
+35+%2B+15+=+50+
+50+=+50+
OK