Question 148075: The manual for your vehicle suggests that you use gasoline that is 89 octane. In order to save some money, you decide to use some 87 octane and some 93 octane in combination with the 89 octane currently in your tank in order to have an approximate 89 octane mixture. Assuming that you have one gallon of 89 octane remaining in your tank (our tank capacity is 16 gallons), how many gallons of 87 and 93 octane should be used to fill up your tank to achieve a mixture of 89 octane? In other words, how many gallons of 87 octane and 93 octane should be used to get 15 gallons of octane (why 15? 16 gallon capacity in tank and one gallon is already in there of 89 octane. You must find the solutions by both the process of substitution and by the process of elimination. Demonstrate both approaches.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In other words, how many gallons of 87 octane and 93 octane should be used to get 15 gallons of octane (why 15?
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Quantity Equation: x + y = 15
Active Ingredient Eq: 87x + 93y = 89*15
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By substitution:
x = 15-y
87(15-y) + 93y = 89*15
6y = 89*15-87*15
y = 30/6
y = 5 (gallons of 93 in the mixture)
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Since x + y = 15, x = 10 (gallons of 87 in the mixture)
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Quantity Equation: x + y = 15
Active Ingredient Eq: 87x + 93y = 89*15
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By elimination:
87x + 87y = 87*15
87x + 93y = 89*15
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Subtract 1st from 2nd to get:
6y = 30
y = 5
Then x = 10
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Cheers,
Stan H.
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