SOLUTION: Suppose you add 70% lemon juice to 1 gallon of 20% lemon juice solution until the mixture becomes 40% lemon juice, how much of the final mixture will you have?

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Question 941069: Suppose you add 70% lemon juice to 1 gallon of 20% lemon juice solution until the mixture becomes 40% lemon juice, how much of the final mixture will you have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+.2%2A1+=+.2+ gallons of lemon juice in 20% mix
Let +x+ = gallons of 70% mix to be added
+.7x+ = gallons of lemon juice in 70% mix
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+%28+.7x+%2B+.2+%29+%2F+%28+x+%2B+1+%29+=+.4+
+.7x+%2B+.2+=+.4%2A%28+x+%2B+1+%29+
+.7x+%2B+.2+=+.4x+%2B+.4+
+.3x+=+.2+
+x+=+2%2F3+
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The final mixture is 1 and 2/3 gallons
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check:
+%28+.7%2A%282%2F3%29+%2B+.2+%29+%2F+%28+2%2F3+%2B+1+%29+=+.4+
+%28+%28+7%2F10+%29%2A%28+2%2F3+%29+%2B+2%2F10+%29+%2F+%28+5%2F3+%29++=+4%2F10+
+7%2F15+%2B+2%2F10+=+10%2F15+
+14%2F30+%2B+6%2F30+=+20%2F30+
+20%2F30+=+20%2F30+
OK