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?

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.