I would like to know if I am correct, so far.
The amount P of pollution varies directly with the population N of people. City A has population of 494,400 and produces 260,000 tons of pollutants. Find how many tons of pollution we should expect City B to produce if population is 344,000. Do not round until final answer. Round to nearest ton.
494,000/260,000=344,000/x
That is the right equation. Do you need a calculator to solve it?
x = 181 tons
shouldn't the answer be 181,000 tons
To solve this problem, we can set up a proportion using the direct variation equation.
The direct variation equation is P = kN, where P represents the amount of pollution, N represents the population, and k is the constant of variation.
We can find the value of k by using the given information about City A: P = 260,000 tons, N = 494,400 people.
260,000 = k * 494,400
To solve for k, divide both sides of the equation by 494,400:
k = 260,000 / 494,400 ≈ 0.5258
Now that we know the value of k, we can use it to find the amount of pollution expected in City B.
We can set up a proportion based on the direct variation equation:
P₁ / N₁ = P₂ / N₂
Where P₁ and N₁ are the values for City A (260,000 and 494,400, respectively), and P₂ and N₂ are the unknowns for City B.
Substituting the known values and the value of k:
260,000 / 494,400 = P₂ / 344,000
To solve for P₂, multiply both sides of the equation by 344,000:
P₂ = (260,000 / 494,400) * 344,000
Calculating this expression, we find:
P₂ ≈ 181,722.66 tons
Finally, we round the answer to the nearest ton:
P₂ ≈ 181,723 tons
Therefore, we should expect City B to produce approximately 181,723 tons of pollution if the population is 344,000.