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.

Question

200 - __ n = 150 - __ n
It will take __ years for the population of moose and mountain goats to be equal.

Answer 1

We can fill in the blanks in your equation as follows:

For the moose:

• The initial population is 200, and it decreases by 15 moose each year. Therefore, we can write this as: \[ 200 - 15n \]

For the mountain goats:

• The initial population is 150, and it decreases by 5 mountain goats each year. Therefore, we can write this as: \[ 150 - 5n \]

Now, we can complete the equation: \[ 200 - 15n = 150 - 5n \]

Next, let's solve this equation for \( n \):

1. Start by moving \( -5n \) to the left side: \[ 200 - 15n + 5n = 150 \] This simplifies to: \[ 200 - 10n = 150 \]

2. Now, isolate the term with \( n \) by subtracting 200 from both sides: \[ -10n = 150 - 200 \] This gives us: \[ -10n = -50 \]

3. Now, divide by -10: \[ n = \frac{-50}{-10} = 5 \]

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

To summarize: \[ 200 - 15n = 150 - 5n \] It will take 5 years for the population of moose and mountain goats to be equal.