word problem

Question

Polluted water is passed through a series of filters. Each filter removes 55% of the remaining impurities from the water. If you have 8 million particles of pollutant per gallon originally, how much pollution will you have after 5 passes through the filters?

Answer 1

Original impurities = X

 

First pass

Impurities removed = 55% * X = 55X/100 = 0.55X

Impurities remaining = X - 0.55X = 0.45X

 

Second pass

Impurities removed = 55% * 0.45X = (55/100) * 0.45X = 0.55 * 0.45X = 0.2475X

Impurities remaining = 0.45X - 0.2475X = 0.2025X

 

Third pass

Impurities removed = 55% * 0.2025X = 0.55 * 0.2025X = 0.111375X

Impurities remaining = 0.2025X - 0,111375X = 0.091125X

 

You can do the fourth and fifth pass on your own. Then you can substitute 8 million for X in impurities remaining after fifth pass to get your answer.