A biologist tracks the numbers of bacteria living in a water tank. the biologist used a function that represents the amount of a certain chemical solution that is added to the water.

-When the water has no chemicals, the number of bacteria (b) is 1200 per gallon.

-For each tablespoon of the chemical solution (c) added to each gallon of water. the number of bacteria decreases by 75 per gallon.

How much of the chemical, in tablespoons, must be added to a 500-gallon tank to reduce the bacteria count to a safe 300 bacteria per gallon?

Question

Mathematics

Jason Hood

14 October, 05:44

A biologist tracks the numbers of bacteria living in a water tank. the biologist used a function that represents the amount of a certain chemical solution that is added to the water.

-When the water has no chemicals, the number of bacteria (b) is 1200 per gallon.

-For each tablespoon of the chemical solution (c) added to each gallon of water. the number of bacteria decreases by 75 per gallon.

How much of the chemical, in tablespoons, must be added to a 500-gallon tank to reduce the bacteria count to a safe 300 bacteria per gallon?

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Answers (1)

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Yuliana Simpson · Answer 1

We let x be the number of tablespoon of chemical solution (c) that is to be added to a certain amount of water. The equation that would best represent the given scenario is,

B = 1200 - 75x

Substituting 300 to B of the equation,

300 = 1200 - 75x

The value of x from the equation is 12. Therefore, 12 tablespoon of chemical should be added per gallon. Since there are 500 gallons of water, the amount of chemical that should be added is 6000 tablespoons.