To extract 1 barrel of oil from the ground requires using 01

To extract 1 barrel of oil from the ground requires using 0.1 barrels of oil and 0.1 kg of steel. To manufacture 1 kg of steel requires 0.05 barrels of oil and 0.01 kg of steel. How many barrels of oil must be extracted from the ground for a net production of 1 metric ton (1,000 kg) of steel with no oil left over at the end?

Solution

Let x be the barrels of oil used and y be the kg of steel.

Then we have x = 0.1x+0.1y

and y =0.05x+0.01y

0.9x = 0.1y or y = 9x

99y = 5x

When y =1000

x =99000/5 = 19800

Hence 19800 barrels of oil should be used.