SOLUTION: Dan mixed 11 liters of cranberry juice into 12 liters of apple juice that had 34 percent sugar. if the cranapple mixture was 43 percent sugar, what was the percent of sugar in the

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Question 1049826: Dan mixed 11 liters of cranberry juice into 12 liters of apple juice that had 34 percent sugar. if the cranapple mixture was 43 percent sugar, what was the percent of sugar in the cranberry juice?


Found 3 solutions by stanbon, josgarithmetic, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
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Dan mixed 11 liters of cranberry juice into 12 liters of apple juice that had 34 percent sugar. if the cranapple mixture was 43 percent sugar, what was the percent of sugar in the cranberry juice?
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Equation:
sugar + sugar = sugar
0.43*11 + 0.34*12 = (x/100)(11 + 12)
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43*11 + 34*12 = 23x
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Ans:: 38.3%
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Cheers,
Stan H.

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The emphasis is on concentration of sugar. 
                   percent sugar        VOLUME       pure sugar
cranberryjuice          p                11          0.01*11*p
applejuice             34                12          0.34*12
MIXTURE                43                23          0.43*23

One way to use this is to account for the amount of pure sugar although the actual way
the concentrations are used is not too clear. Was that as mass per volume? This would
not be appropriate with such high concentrations of sugar. The rest of this problem-solving
may be faulty because of this need for the right kind of percentage. Sugar itself would
be a solid, so counting it in mass would be used. Your description did not say. The concentration
must either be volume per volume (which makes no sense here), or mass per mass (but no density were
given), or mass per volume (but this seems poor to use for such high sugar concentrations).

Going ahead with just the arithmetic, accounting for the sugar:
highlight_green%280.01%2A11p%2B0.34%2A12=0.43%2A23%29
Solve for p.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = liters of sugar in the cranberry juice
+.34%2A12+=+4.08+ = liters of sugar in the apple juice
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+%28+x+%2B+4.08+%29+%2F+%28+11+%2B+12+%29+=+.43+
++x+%2B+4.08++=+.43%2A23+
++x+=+9.89+-+4.08+
+x+=+5.81+ liters
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Find % of sugar in cranberry juice
+%28+5.81%2F11+%29%2A100+=+52.82+
52.82% sugar in cranberry juice
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