SOLUTION: A new automobile engine can run on a mixture of gasoline and a substitute fuel. If gas costs $3.25 per gallon and the substitute costs 90¢ per gallon, what percent of a mixture mus

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Question 990545: A new automobile engine can run on a mixture of gasoline and a substitute fuel. If gas costs $3.25 per gallon and the substitute costs 90¢ per gallon, what percent of a mixture must be substitute to bring the cost down to $3.00 per gallon?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = gallons of gasoline used
Let +b+ = gallons of substitute used
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I will say that I am filling a 100 gallon
tank with the mixture
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(1) +a+%2B+b+=+100+
(2) +%28+325a+%2B+90b+%29+%2F+100+=+300+ ( in cents )
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(2) +325a+%2B+90b+=+30000+
(2) +65a+%2B+18b+=+6000+
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Multiply both sides of (1) by +18+ and
subtract (1) from (2)
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(2) +65a+%2B+18b+=+6000+
(1) +-18a+-+18b+=+-1800+
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+47a+=+4200+
+a+=+89.362+
and
(1) +a+%2B+b+=+100+
(1) +b+=+10.638+
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10.638 % of substitute and 89.362 % of gasoline
must be used
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check answer:
(2) +%28+325a+%2B+90b+%29+%2F+100+=+300+
(2) +%28+325%2A89.362+%2B+90%2A10.638+%29+%2F+100+=+300+
(2) ++29042.65+%2B+957.42+=+30000+
(2) +30000.07+=+30000+
error due to rounding off