The amount P of population varies directly with the population N of people. City A has a population of 416,000 and produces 260,000 tons of pollutants. Find how many tons of pollution we should expect City B to produce, if we know that its population is 350,000. (Show all work and do not round until the final answer. Then round to the nearest ton as needed)

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Hi Theresa,

Direct variation means the ratio is a constant. So, you have

P/N = constant

260,000/416,000 = P/350,000

Solve for P,

P = 218,750 tons of pollutants

Hope it helps you!

When two variables vary "directly", it means that they fit into the equation y=mx, where y varies directly with x, with the multiplier m to be determined by the information you are given.

For this problem, P (pollutants) varies directly with N (people) so the equation is P=mN for their relation.

You are given that City A has P = 260,000 tons of pollutants and N = 416,000 people. Plug these into the equation above (P=mN) and you get 260,000=(m)(416,000). If we divide each side by 416,000, you get that m=0.625. So now you have the multiplier for your equation: P=(0.625)N.

Use the complete equation now to find out how many P (pollutants) City B will produce.

P=(0.625)N

P=(0.625)(350,000) [[350,000 was the given "N" or amount of people in City B]]

P=218,750 tons of pollutants

We should expect 218,750 tons of pollutants from City B.

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