#22 Solve the following systems of equations: 18. 10x - 2y = -13 -2x + 3y= 13 19

Question

#22

Solve the following systems of equations: 18. 10x - 2y = -13 -2x + 3y= 13 19. x - 2y = -1 -3x + 6y = 5 20. x + 6y + 3z = 4 2x + y + 2z = 3 3x - 2y + z =0 21. 2x + 2y + z = 6 4x - 3y + z = -8 -2x - 6z = 5 A company produces Italian sausages and bratwursts at plants in Green Bay and Sheboygan, WI. The Green Bay plant can produce 800 Italian sausages per hour and 800 bratwursts per hour. The Sheboygan plant can produce 500 Italian sausages per hour and 1000 bratwursts per hour. How many hours should each plant operate to fill an order of exactly 62, 250 Italian sausages and 76.500 bratwursts?

Explanation / Answer

Let X be the number of hours the green bay plant operates and Y be the number of hours the Sheboygan plane operates. Then,

As green bay plant can produce 800 Italian sausages per hour and 800 bratwursts per hour, and the Sheboygan plant can produce 500 Italian sausages per hour and 1000 bratwursts per hour. Therefore we get:

800X + 500Y = 62250

800X + 1000Y = 76500

Subtract the first equation from the second one we get:

500Y = 76500 - 62250 = 14250

Therefore we get:

Y = 14250/500 = 28.5

Putting this in first equation we get:

800X + 500Y = 62250

800X + 500*28.5 = 62250

800X = 62250 - 14250

Therefore we get: X = 60

Therefore the Green Bay plant should operate for 60 hours and Sheboygan plant should operate for 28.5 hours.

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