Question 87956: Word problem:
20 gallons of fuel and 14 gallons of collant cost $12,000 - needed for first simulation test
15 gallons of fuel and 9 gallons of coolant cost $8,000 - needed for second simulation test
What is the cost per gallon of fuel and a collant tank for the project?
Steps
1. assign variables
2. write algebraic model
3. solve model
4. answer
thanks
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Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Word problem:
20 gallons of fuel and 14 gallons of collant cost $12,000 - needed for first simulation test
15 gallons of fuel and 9 gallons of coolant cost $8,000 - needed for second simulation test
What is the cost per gallon of fuel and a collant tank for the project?
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20f + 14c = 12000
15f + 9c = 8000
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Multiply 1st equation by 3 and 2nd equation by 4 to get:
60f + 42c = 36000
60f + 36c = 32000
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Subtract the 2nd equation from the 1st to solve for c, as follows:
6c = 4000
c = $666.67 (Cost of a gallon of coolant)
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Substitute to solve for f, as follows:
20f + 14*666.67 = 12000
20f + 9333.33 = 12000
20f = 10666.67
f = $533.33 (Cost of a gallon of fuel)
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Cheers,
Stan H.
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