SOLUTION: A bottle of fruit juice contains 10% water. How much water must be added to this to produce 7 L of fruit juice that is 55% water?

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Question 687757: A bottle of fruit juice contains 10% water. How much water must be added to this to produce 7 L of
fruit juice that is 55% water?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In +7+ liters of juice that contains 55% water, there is
+.55%2A7+=+3.85+ liters of water
Let +w+ = liters of water to be added
+7+-+w+ = liters of juice before adding water
+.1%2A%28+7+-+w+%29+ = liters of water at the beginning
----------------
( liters of water you end up with ) / ( liters of juice you end up with ) = .55
+%28+.1%2A%28+7+-+w+%29+%2B+w+%29+%2F+7+=+.55+
+%28+.7+-+.1%2Aw+%2B+w+%29+%2F+7+=+.55+
+%28+.7+%2B+.9w+%29+%2F+7+=+.55+
+.7+%2B+.9w+=+.55%2A7+
+.9w+=+3.85+-+.7+
+.9w+=+3.15+
+w+=+3.5+
3.5 liters of water need to be added
check:
+.1%2A%28+7+-+w+%29+ = liters of water at the beginning
+.1%2A%28+7+-+3.5+%29++=+.35+ liters
--------------------------
In +7+ liters of juice that contains 55% water, there is
+.55%2A7+=+3.85+ liters of water
( liters of water you end up with ) - ( liters of water started with ) = ( liters of water to be added )
+3.85+-+.35+=+3.5+ liters of water added