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
Q. 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
Set Up Equation: Let's denote the number of years from today as y. 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 y years.Canyon Falls population after y years: 22,500−740ySwift Creek population after y years: 15,200+1,500yThe equation we need to solve is:15,200+1,500y=2(22,500−740y)
Distribute 2: Now, let's distribute the 2 on the right side of the equation:15,200+1,500y=45,000−1,480y
Combine Like Terms: Next, we combine like terms by adding 1,480y to both sides of the equation and subtracting 15,200 from both sides:15,200+1,500y+1,480y=45,000−1,480y+1,480y15,200−15,200+2,980y=45,000−15,2002,980y=29,800
Solve for y: Now, we solve for "y" by dividing both sides of the equation by 2,980: y=2,98029,800
Perform Division: Performing the division gives us the number of years: y=10
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