In order to meet a certain octane number specification, it is necessary to produ

Question

In order to meet a certain octane number specification, it is necessary to produce a gasoline containing 83% (by weight) isooctane and 17% n-heptane. How many gallons of high-octane gasoline containing 92% isooctane and 8% n-heptane must be blended with straight-run gasoline containing 63% isooctane and 37% n-heptane to obtain 10,000 gal of the desired gasoline? The density of each of the liquids is 6.7 lb/gal. In order to meet a certain octane number specification, it is necessary to produce a gasoline containing 83% (by weight) isooctane and 17% n-heptane. How many gallons of high-octane gasoline containing 92% isooctane and 8% n-heptane must be blended with straight-run gasoline containing 63% isooctane and 37% n-heptane to obtain 10,000 gal of the desired gasoline? The density of each of the liquids is 6.7 lb/gal.

Explanation / Answer

Answer

Say amount high octane gasoline required is H and low octane is L

To prepare 100 lb of  the required gasoline, we have

63L + 92H = 83 and 37L + 8H = 17. Two equations and two unknows. Solving this, we have

L = 31 and H = 69.

10000 gal = 67000 lb

Therefore to prepare 10000 gal of required gasoline, we need to mix 69*67000/100 = 46230 lb of High octane with 20770 lb of low octane

in other words, 3100 gallons of Low octane should be mixed with 6900 gallons of high octane.

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