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.

Answer 1

To find the number of years it will take for the populations of moose and mountain goats to be equal, we can set up equations to represent their populations over time.

Let \( n \) be the number of years.

Moose Population:

The initial population of moose is 200, and it is decreasing by 15 moose each year. The equation for the moose population after \( n \) years is: \[ \text{Moose population} = 200 - 15n \]

Mountain Goat Population:

The initial population of mountain goats is 150, and it is decreasing by 5 mountain goats each year. The equation for the mountain goat population after \( n \) years is: \[ \text{Mountain goat population} = 150 - 5n \]

Setting the Equations Equal:

We need to find the number of years (\( n \)) when the populations are equal: \[ 200 - 15n = 150 - 5n \]

Solving the Equation:

1. First, add \( 15n \) to both sides: \[ 200 = 150 - 5n + 15n \] Simplifies to: \[ 200 = 150 + 10n \]

2. Next, subtract 150 from both sides: \[ 50 = 10n \]

3. Finally, divide both sides by 10: \[ n = 5 \]

Conclusion:

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