Question

Question

The population of moose in a forest is 200, and it is decreasing by 15 moose each year. In the same forest, there are 150 mountain goats. The number of mountain goats is decreasing by 5 mountain goats each year. Let n
be the number of years. Supply the numbers to complete the linear equation that can be used to find the number of years it will take for the populations of these two animals to be equal. Then, solve the equation.(2 points)
200−
n=150−
n

It will take
years for the population of moose and mountain goats to be equal.

Answer 1

To find the equation for the populations of moose and mountain goats over time, we have the following initial populations and rates of decrease:

• Moose: Initial population = 200, decrease = 15 moose/year
• Mountain Goats: Initial population = 150, decrease = 5 mountain goats/year

The formulas for each population after \( n \) years will be:

• Moose population after \( n \) years: \( 200 - 15n \)
• Mountain goat population after \( n \) years: \( 150 - 5n \)

We set these populations equal to each other to find when they will be the same:

\[ 200 - 15n = 150 - 5n \]

Now, we will solve for \( n \).

1. First, let's simplify the equation: \[ 200 - 150 = 15n - 5n \] \[ 50 = 10n \]

2. Now, divide both sides by 10: \[ n = \frac{50}{10} = 5 \]

Thus, it will take 5 years for the populations of moose and mountain goats to be equal.