SOLUTION: How do i solve the following word problem? Sally and her friends are making lemonade to sell at a carnival. Sally made a strong lemonade with 50% lemon juice. Her friend Janet

Algebra ->  Equations -> SOLUTION: How do i solve the following word problem? Sally and her friends are making lemonade to sell at a carnival. Sally made a strong lemonade with 50% lemon juice. Her friend Janet      Log On


   



Question 751374: How do i solve the following word problem?
Sally and her friends are making lemonade to sell at a carnival. Sally made a strong lemonade with 50% lemon juice. Her friend Janet made hers weaker with only 25% lemon juice. They decided to compromise and make some lemonade that is 35% lemon juice. How much of the 25% lemonade must be used to make 10L at this new percentage.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 50% lemonade needed
Let +b+ = liters of 25% lemonade needed
+.5a+ = liters of lemon juice in 50% lemonade
+.25b+ = liters of lemon juice in 25% lemonade
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(1) +a+%2B+b+=+10+
(2) +%28+.5a+%2B+.25b+%29+%2F+10+=+.35+
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(2) +.5a+%2B+.25b+=+3.5+
(2) +50a+%2B+25b+=+350+
(2) +2a+%2B+b+=+14+
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Subtract (1) from (2)
(2) +2a+%2B+b+=+14+
(1) +-a+-+b+=+-10+
+a+=+4+
and, since
(1) +a+%2B+b+=+10+
(1) +b+=+6+
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6 liters of 25% lemonade is needed
check:
(2) +%28+.5%2A4+%2B+.25%2A6+%29+%2F+10+=+.35+
(2) +%28+2+%2B+1.5+%29+%2F+10+=+.35+
(2) +3.5+=+.35%2A10+
(2) +3.5+=+3.5+
OK