SOLUTION: I am a little confused. Please help: Smith wants to make a 100 quarts of 5% chocolate milk solution mixing a quantity of a 2% chocolate milk solution with a quantity of 7% choco

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Question 794667: I am a little confused. Please help:
Smith wants to make a 100 quarts of 5% chocolate milk solution mixing a quantity of a 2% chocolate milk solution with a quantity of 7% chocolate milk solution. What is the quantity of the 7% that he has to use?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = quarts of 7% chocolate milk needed
+.07a+ = quarts of pure chocolate in 7% chocolate milk
Let +b+ = quarts of 2% chocolate milk needed
+.02b+ = quarts of pure chocolate in 2% chocolate milk
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given:
(1) +a+%2B+b+=+100+
(2) +%28+.07a+%2B+.02b+%29+%2F+100+=+.05+
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(2) +.07a+%2B+.02b+=+5+
(2) +7a+%2B+2b+=+500+
Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +7a+%2B+2b+=+500+
(1) +-2a+-+2b+=+-200+
+5a+=+300+
+a+=+60+
and, since
(1) +a+%2B+b+=+100+
(1) +60+%2B+b+=+100+
(1) +b+=+40+
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60 quarts of 7% chocolate milk are needed
40 quarts of 2% chocolate milk are needed
check answer:
(2) +%28+.07a+%2B+.02b+%29+%2F+100+=+.05+
(2) +%28+.07%2A60+%2B+.02%2A40+%29+%2F+100+=+.05+
You can finish this check