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

Question

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.

200 −___n = 150 −___n

Answer 1

To express the populations of moose and mountain goats over time in years \( n \), we can set up the following equations based on the information given:

1. The initial population of moose is 200, and it decreases by 15 moose each year: \[ \text{Population of moose after } n \text{ years} = 200 - 15n \]

2. The initial population of mountain goats is 150, and it decreases by 5 mountain goats each year: \[ \text{Population of mountain goats after } n \text{ years} = 150 - 5n \]

We want to find the time \( n \) when the populations become equal, which gives us the equation: \[ 200 - 15n = 150 - 5n \]

Now, let's complete the linear equation with the correct values: \[ 200 - 15n = 150 - 5n \]

To solve this equation, we first rearrange it:

1. Add \( 15n \) to both sides: \[ 200 = 150 - 5n + 15n \]
2. Combine like terms: \[ 200 = 150 + 10n \]
3. Subtract 150 from both sides: \[ 200 - 150 = 10n \] \[ 50 = 10n \]
4. Divide by 10: \[ n = 5 \]

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