SOLUTION: A bottle of juice contains 20% water. how muck water must be added to the bottle to produce 8 L of fruit juice that id 59% water?

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Question 926786: A bottle of juice contains 20% water. how muck water must be added to the bottle to produce 8 L of fruit juice that id 59% water?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of original solution
Let +b+ = liters of water to be added
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+.2a+ = liters of water in original solution
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+8+ L of 59% water =
+.59%2A8+=+4.72+ L of water
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(1) +a+%2B+b+=+8+
(2) +.2a+%2B+b+=+4.72+
----------------------
(2) +20a+%2B+100b+=+472+
(2) +5a+%2B+25b+=+118+
----------------------
Multiply both sides of (1) by +5+
and subtract (1) from (2)
(2) +5a+%2B+25b+=+118+
(1) +-5a+-+5b+=+-40+
----------------------
+20b+=+78+
+b+=+3.9+
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3.9 L of water should be added
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check:
(1) +a+%2B+b+=+8+
(1) +a+=+8+-+3.9+
(1) +a+=+4.1+
-----------------
(2) +.2a+%2B+b+=+4.72+
(2) +.2%2A4.1+%2B+3.9+=+4.72+
(2) +.82+%2B+3.9+=+4.72+
(2) +4.72+=+4.72+
OK