Question

# Five hundred gallons of 89-octane gasoline is obtained by mixing 87-octane gasoline with 92-octane gasoline. How much of each type of gasoline is required to obtain the 500 gallons of 89-octane gasoline?

Solution

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$\left\{ \begin{array}{lr} x+y=500 \\ .87x+.92y =(.89)(500) \end{array} \right.$

Let $x$ equal the gallons of 87-octane gasoline and $y$ equal the gallons of 92-octane gasoline. The first equation represents the sum of the two types of gasoline equaling 500 gallons. The second equation represents the amount of 87- and 92-octane gasolines in the final mixture.

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