SOLUTION: A grocer mixed Apple juice that costs $12.50 per gallon with 25 gallons of cranberry juice that costs $31.50 per gallon. How much apple juice was used to make cran-apple juice cost

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Question 1101350: A grocer mixed Apple juice that costs $12.50 per gallon with 25 gallons of cranberry juice that costs $31.50 per gallon. How much apple juice was used to make cran-apple juice costing $25 per gallon?
Found 4 solutions by stanbon, josmiceli, ikleyn, richwmiller:
Answer by stanbon(75887) About Me  (Show Source):
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A grocer mixed Apple juice that costs $12.50 per gallon with 25 gallons of cranberry juice that costs $31.50 per gallon. How much apple juice was used to make cran-apple juice costing $25 per gallon?
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value + value = value
12.5x +31.5*25 = 25*(x+25)
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125x + 315*25 = 250x + 250*25
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125x = 65*25
5x = 65
x = 13 gallons (amt. of apple juice needed)
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
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Let +x+ = gallons of apple juice needed
+%28+12.5x+%2B+31.5%2A25+%29+%2F+%28+x+%2B+25+%29+=+25+
+12.5x+%2B+787.5+=+25%2A%28+x+%2B+25+%29+
+12.5x+%2B+787.5+=+25x+%2B+625+
+12.5x+=+162.5+
+x+=+13+
13 gallons of apple juice are needed
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check:
+%28+12.5x+%2B+787.5+%29+%2F+%28+x+%2B+25+%29+=+25+
+12.5%2A13+%2B+787.5+=+25%2A%28+13+%2B+25+%29+
+162.5+%2B+787.5+=+25%2A38+
+950+=+950+
OK

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
l
The correct answer is
    13 gallons of apple juice are needed.


Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
check 13 gallons
13*12.50+25*31.50=(13+25)*25
162.5+787.5=38*25
950=950
ok 13 gallons
check 17 gallons
17*12.50+25*31.50=(17+25)*25
212.5+787.5=42*25
1000=1050
not ok 17 gallons
Stan's error was 315-250=65 not 85
125x = 85*25 should have been
125x = 65*25
5x=65
x=13