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Today, the population of Canyon Falls is 22,500 and the population of Swift Creek is 15,200 . The population of Canyon Falls is decreasing at the rate of 740 people each year while the population of Swift Creek is increasing at the rate of 1,500 people each year. Assuming these rates continue into the future, in how many years from today will the population of Swift Creek equal twice the population of Canyon Falls?
Choose 1 answer:
(A) 9 years
(B) 
10 years
(C) 
11 years
(D) 12 years

Today, the population of Canyon Falls is 2222,500500 and the population of Swift Creek is 1515,200200 . The population of Canyon Falls is decreasing at the rate of 740740 people each year while the population of Swift Creek is increasing at the rate of 11,500500 people each year. Assuming these rates continue into the future, in how many years from today will the population of Swift Creek equal twice the population of Canyon Falls?\newlineChoose 11 answer:\newline(A) 99 years\newline(B) 10 \mathbf{1 0} years\newline(C) 11 \mathbf{1 1} years\newline(D) 1212 years

Full solution

Q. Today, the population of Canyon Falls is 2222,500500 and the population of Swift Creek is 1515,200200 . The population of Canyon Falls is decreasing at the rate of 740740 people each year while the population of Swift Creek is increasing at the rate of 11,500500 people each year. Assuming these rates continue into the future, in how many years from today will the population of Swift Creek equal twice the population of Canyon Falls?\newlineChoose 11 answer:\newline(A) 99 years\newline(B) 10 \mathbf{1 0} years\newline(C) 11 \mathbf{1 1} years\newline(D) 1212 years
  1. Set Up Equation: Let's denote the number of years from today as yy. We need to set up an equation that represents the situation where the population of Swift Creek equals twice the population of Canyon Falls after yy years.\newlineCanyon Falls population after yy years: 22,500740y22,500 - 740y\newlineSwift Creek population after yy years: 15,200+1,500y15,200 + 1,500y\newlineThe equation we need to solve is:\newline15,200+1,500y=2(22,500740y)15,200 + 1,500y = 2(22,500 - 740y)
  2. Distribute 22: Now, let's distribute the 22 on the right side of the equation:\newline15,200+1,500y=45,0001,480y15,200 + 1,500y = 45,000 - 1,480y
  3. Combine Like Terms: Next, we combine like terms by adding 1,480y1,480y to both sides of the equation and subtracting 15,20015,200 from both sides:\newline15,200+1,500y+1,480y=45,0001,480y+1,480y15,200 + 1,500y + 1,480y = 45,000 - 1,480y + 1,480y\newline15,20015,200+2,980y=45,00015,20015,200 - 15,200 + 2,980y = 45,000 - 15,200\newline2,980y=29,8002,980y = 29,800
  4. Solve for y: Now, we solve for "y" by dividing both sides of the equation by 2,9802,980: \newliney=29,8002,980y = \frac{29,800}{2,980}
  5. Perform Division: Performing the division gives us the number of years: y=10y = 10