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17 December, 08:20

An oil company operates two Southern refineries. The Alabama facility produces 500 barrels of high-grade oil and 200 barrels of medium-grade oil per day. The Texas facility produces 600 barrels of high-grade and 400 barrels of medium-grade oil per day. By operating each facility for a certain number of days, the company produces exactly 15,000 barrels of high-grade and 8400 barrels of medium-grade oil. How many days must each facility operate to produce the desired result?

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  1. 17 December, 08:45
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    Call x the number of days the Alabama facility operares and y the number of days the Texas facility operates

    Number of barrels produced:

    Facility Alabama Texas total

    HIgh grade production: 500x 600y 15,000

    Medium grade production 200x 400y 8,400

    Equations

    500x + 600y = 15,000

    200x + 400y = 8400

    Divide each equation by 100

    5x + 6y = 150

    2x + 4y = 84

    Multiply first by 2 and second by 5 = >

    10x + 12y = 300

    10x + 20y = 420

    Subtract the first from the second:

    20y - 12y = 420 - 300

    8y = 120

    y = 120/8

    y = 15

    Replace y value on any of the equations:

    2x + 4y = 84 = > 2x = 84 - 8y =

    2x = 84 - 4 (15)

    2x = 84 - 60

    2x = 24

    x = 24/x

    x = 12

    Answer: the Alabama facility must operate 12 days and the Texas facility must operate 15 days.
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