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Math Word problem

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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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
Check Marked as Best Answer
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!
Erica M. | Tutor for: Math, Science, SAT, Programs: iMovie, FinalCut, AdobeTutor for: Math, Science, SAT, Programs:...
4.9 4.9 (22 lesson ratings) (22)
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)(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.