SOLUTION: Stan Wellback wants to make 5 gallons of 55% gas, 45% oil mixture of fuel for his dirt bike. he has two containers, container A is 95% gasoline, 5%oil and container B is 10% gas, 9

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Question 560098: Stan Wellback wants to make 5 gallons of 55% gas, 45% oil mixture of fuel for his dirt bike. he has two containers, container A is 95% gasoline, 5%oil and container B is 10% gas, 90% oil. How many gallons (to the nearest tenth) does he need from each container to make his new mixture?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = gallons of mixture needed from container A
Let b = gallons of mixture needed from container B
+.95a+ = gallons of gas in container A
+.1B+ = gallons of gas in container B
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(1) +a+%2B+b+=+5+
(2) +%28+.95a+%2B+.1b+%29+%2F+5+=+.55+
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(2) +.95a+%2B+.1b+=+2.75+
(2) +95a+%2B+10b+=+275+
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Multiply both sides of (1) by +10+
and subtract (1) from (2)
(2) +95a+%2B+10b+=+275+
(1) +-10a+-10+b+=+-50+
+85a+=+225+
+a+=+2.647+
and, since
(1) +a+%2B+b+=+5+
(1) +2.647+%2B+b+=+5+
(1) +b+=+5+-+2.647+
(1) +b+=+2.353+
He needs 2.6 gallons from container A
and 2.4 gallons from container B
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check answer:
(2) +%28+.95%2A2.647+%2B+.1%2A2.353+%29+%2F+5+=+.55+
(2) +%28+2.515+%2B+.235+%29+%2F+5+=+.55+
(2) +2.75+%2F+5+=+.55+
(2) +2.75+=+.55%2A5+
(2) +2.75+=+2.75+
OK